Here's an excellent quote from St. Alphonsus (another great Doctor of the Church) in his book The History of Heresies and Their Refutation on Pope Honorius:

“Not alone the heretical, but even some Catholic writers, have judged, from these expressions of Pope Honorius, that he fell into the Monothelite heresy; but they are certainly deceived; because when he says that there is only one will in Christ, he intends to speak of Christ as man alone, and in that sense, as a Catholic, he properly denies that there are two wills in Christ opposed to each other, as in us the flesh is opposed to the spirit; and if we consider the very words of his letter, we will see that such is his meaning. ‘We confess one will alone in Jesus Christ, for the Divinity did not assume our sin, but our nature, as it was created before it was corrupted by sin.’ This is what Pope John IV. writes to the Emperor Constantine II., in his apology for Honorius: ‘Some,’ said he, ‘admitted two contrary wills in Jesus Christ, and Honorius answers that by saying that Christ—perfect God and perfect man—having come to heal human nature, was conceived and born without sin, and therefore, never had two opposite wills, nor in him the will of the flesh ever combated the will of the spirit, as it does in us, on account of the sin contracted from Adam.’ He therefore concludes that those who imagine that Honorius taught that there was in Christ but one will alone of the Divinity and of the humanity, are at fault. St. Maximus, in his dialogue with Pyrrhus, and St. Anastasius Bibliothecarius, make a similar defence for Honorius. Graveson, in confirmation of this, very properly remarks, that as St. Cyril, in his dispute with Nestorius, said, in a Catholic sense, that the nature of the Incarnate Word was one, and the Eutychians seized on the expression as favourable to them, in the same manner, Honorius saying that Christ had one will (that is, that he had not, like us, two opposite wills—one defective, the will of the flesh, and one correct, the will of the Spirit), the Monothelites availed themselves of it to defend their errors.

 
We do not, by any means, deny that Honorius was in error, when he imposed silence on those who discussed the question of one or two wills in Christ, because when the matter in dispute is erroneous, it is only favouring error to impose silence. Wherever there is error it ought to be exposed and combated, and it was here that Honorius was wrong; but it is a fact beyond contradiction, that Honorius never fell into the Monothelite heresy, notwithstanding what heretical writers assert, and especially William Cave, who says it is labour in vain to try and defend him from his charge. The learned Noel Alexander clearly proves that it cannot be laid to his charge, and in answer to the great argument adduced by our adversaries, that in the Thirteenth Act of the Sixth Council it was declared that he was anathematized—replies that the Synod condemned Honorius, not because he formally embraced the heresy, but on account of the favour he showed the heretics, as Leo II. (Optimo Concilii Interpreter as N. Alex, calls him) writes to Constantine Pogonatus in his Epistle, requesting the confirmation of the Synod. In this letter Leo enumerates the heretics condemned, the fathers of the heresy, Theodore of Pharan, Cyrus of Alexandria, Sergius, Pyrrhus, Paul and Peter, successors in the See of Constantinople; he also anathematizes Honorius, not for embracing the error, but for permitting it to go on unmolested . . . He also writes to the Spanish bishops, and tells them that Theodore, Cyrus, and the others are condemned, together with Honorius, who did not, as befitted his Apostolical authority, extinguish the flame of heretical doctrine in the beginning, but cherished it by negligence. From these and several other sources, then, Noel Alexander proves that Honorius was not condemned by the Sixth Council as a heretic, but as a favourer of heretics, and for his negligence in putting them down, and that he was very properly condemned, for the favourers of heresy and the authors of it are both equally culpable. He adds that the common opinion of the Sorbonne was, that although Honorius, in his letters, may have written some erroneous opinions, still he only wrote them as a private doctor, and in no wise stained the purity of the faith of the Apostolic See; and his letters to Sergius, which we quoted in the last paragraph, prove how different his opinions were from those of the Monothelites.”

Here's an excellent quote from St. Alphonsus (another great Doctor of the Church) in his book The History of Heresies and Their Refutation on Pope Honorius:

“Not alone the heretical, but even some Catholic writers, have judged, from these expressions of Pope Honorius, that he fell into the Monothelite heresy; but they are certainly deceived; because when he says that there is only one will in Christ, he intends to speak of Christ as man alone, and in that sense, as a Catholic, he properly denies that there are two wills in Christ opposed to each other, as in us the flesh is opposed to the spirit; and if we consider the very words of his letter, we will see that such is his meaning. ‘We confess one will alone in Jesus Christ, for the Divinity did not assume our sin, but our nature, as it was created before it was corrupted by sin.’ This is what Pope John IV. writes to the Emperor Constantine II., in his apology for Honorius: ‘Some,’ said he, ‘admitted two contrary wills in Jesus Christ, and Honorius answers that by saying that Christ—perfect God and perfect man—having come to heal human nature, was conceived and born without sin, and therefore, never had two opposite wills, nor in him the will of the flesh ever combated the will of the spirit, as it does in us, on account of the sin contracted from Adam.’ He therefore concludes that those who imagine that Honorius taught that there was in Christ but one will alone of the Divinity and of the humanity, are at fault. St. Maximus, in his dialogue with Pyrrhus, and St. Anastasius Bibliothecarius, make a similar defence for Honorius. Graveson, in confirmation of this, very properly remarks, that as St. Cyril, in his dispute with Nestorius, said, in a Catholic sense, that the nature of the Incarnate Word was one, and the Eutychians seized on the expression as favourable to them, in the same manner, Honorius saying that Christ had one will (that is, that he had not, like us, two opposite wills—one defective, the will of the flesh, and one correct, the will of the Spirit), the Monothelites availed themselves of it to defend their errors.

 
We do not, by any means, deny that Honorius was in error, when he imposed silence on those who discussed the question of one or two wills in Christ, because when the matter in dispute is erroneous, it is only favouring error to impose silence. Wherever there is error it ought to be exposed and combated, and it was here that Honorius was wrong; but it is a fact beyond contradiction, that Honorius never fell into the Monothelite heresy, notwithstanding what heretical writers assert, and especially William Cave, who says it is labour in vain to try and defend him from his charge. The learned Noel Alexander clearly proves that it cannot be laid to his charge, and in answer to the great argument adduced by our adversaries, that in the Thirteenth Act of the Sixth Council it was declared that he was anathematized—replies that the Synod condemned Honorius, not because he formally embraced the heresy, but on account of the favour he showed the heretics, as Leo II. (Optimo Concilii Interpreter as N. Alex, calls him) writes to Constantine Pogonatus in his Epistle, requesting the confirmation of the Synod. In this letter Leo enumerates the heretics condemned, the fathers of the heresy, Theodore of Pharan, Cyrus of Alexandria, Sergius, Pyrrhus, Paul and Peter, successors in the See of Constantinople; he also anathematizes Honorius, not for embracing the error, but for permitting it to go on unmolested . . . He also writes to the Spanish bishops, and tells them that Theodore, Cyrus, and the others are condemned, together with Honorius, who did not, as befitted his Apostolical authority, extinguish the flame of heretical doctrine in the beginning, but cherished it by negligence. From these and several other sources, then, Noel Alexander proves that Honorius was not condemned by the Sixth Council as a heretic, but as a favourer of heretics, and for his negligence in putting them down, and that he was very properly condemned, for the favourers of heresy and the authors of it are both equally culpable. He adds that the common opinion of the Sorbonne was, that although Honorius, in his letters, may have written some erroneous opinions, still he only wrote them as a private doctor, and in no wise stained the purity of the faith of the Apostolic See; and his letters to Sergius, which we quoted in the last paragraph, prove how different his opinions were from those of the Monothelites.”

So Honorius can in no way be equated with the post-conciliar popes.  He remained a pope because he was never a heretic.

Well as one theologian noted, it is incontrovertible that pope honorious was condemned by a council as a heretic.

It is claimed that he was condemned by a handful of councils, which Pope Adrian II and Leo II even agreed with, and that Pope Agatho even declared anathema to Honorius and the monothelites. St. Robert knows all this. He  explains the councils' acts by arguing they were fabrications or corruptions introduced by heretics.

In defense, he writes:

Thirdly, the Council could not condemn Honorius as a heretic, unless it opposed the epistle of St. Agatho, nay, more even itself and plainly asserts the contrary. For Pope Agatho in Epistle I to the Emperor, which was read in that very Council (sess. 4) he says…the faith in the see of Peter did not fail, nor could fail, and hence the Pope cannot, as Pope, settle something against the faith: but even all his predecessors, one of which is Honorius, always resisted heresies, and strengthened the brethren in faith.
…
Therefore, from these testimonies I argue: If Honorius was a Monothelite heretic, how could Agatho disputing in the face of which concerning this very heresy, write that none of his predecessors ever erred? And when the other Churches were stained by the errors of their Prelates, only the Roman Church remained intact? Then, if the Council affirmed that Peter spoke through Agatho, and said: “the Roman Pontiffs always confirmed their brethren in faith, and never succuмbed to heresy,” with what temerity would the same Council in nearly each action say anathema to the heretic Honorius? Therefore it must be that either the Council was falsified; or the epistle of Agatho, or that the Council is opposed with itself and with Agatho. Now this last one nobody has ever asserted, not even the heretics; on the second there was never any suspicion; therefore it is necessary to hold the first.

Whether or not st. Bellarmine had difficulty, hundreds of years afterwards, reconciling this fact with the honour that he ascribed to the holder of the papal office is besides the point.

So what? Popes have more authority than councils, and councils cannot depose a valid pope.