First, I do not assume they are popes, I believe they are popes - why? because that is the Catholic default position. This default position, among other things, is based on reality. 

I already know the sedes believe that "the Popes have not taught error or promulgated a harmful / offensive Mass ... BECAUSE THEY ARE NOT POPES." Everybody knows this. They believe this even though their starting (and ending) point, i.e. the MAJOR, is wrong. IOW, their opinion-turned-doctrine is based on a false premise per the Council of Constantinople. This false premise is the sede default position.

I'm now waiting for you to start calling both Pope Agatho and Pope Leo II old catholic heretics and condemn the whole Third Council of Constantinople while you're at it. 

Pope Honorius I

Pope (625-12 October, 638), a Campanian, consecrated 27 October (Duchesne) or 3 November (Jaffé, Mann), in succession to Boniface V. His chief notoriety has come to him from the fact that he was condemned as a heretic by the sixth general council (680)

And if one were to deny Honorius was condemned and anathematized, one would also have to deny the authority and affirmation of the Fourth Council of Constantinople (Eighth Ecuмenical), because it explicitly confirms the Sixth Council’s condemnations.

“Further, we accept the sixth, holy and universal synod {6 Constantinople III}, which shares the same beliefs and is in harmony with the previously mentioned synods in that it wisely laid down … So, we anathematize Theodore … and with these, Honorius of Rome, Cyrus of Alexandria as well as Macarius of Antioch and his disciple Stephen, who followed the false teachings of the unholy heresiarchs…”

— Definition of the holy and universal Eighth Synod (Fourth Council of Constantinople, 869–870)

This is very controversial history.

I would simply say that no one should be too ready to consider Pope Honorius to have been a heretic without first reading St Robert Bellarmine's very thorough consideration of the question in his defence.

In relation to this affirmation, in particular, St Robert has this answer:

What if someone were brought in that could not believe that the Sixth Council would be corrupted; he could look to another solution, which is in Juan de Torquemada. He teaches that the Fathers of the Sixth Council condemned Honorius but from false information, and hence erred in that judgement. Although a legitimate general council could not err in defining dogmas of faith (and the Sixth council did not), still it could err in questions of fact. Therefore, we can safely say that those Fathers were deceived by false rumours and did not understand the epistles of Honorius, and wrongly enumerated Honorius with the heretics.

So one would not have to deny the authority of these councils. We are not dealing with definitions of faith or morals.

Thank you PV!

Hey "Catholic Trumpet guy (AL)" dare we hope that you will say...

However, the question at issue is not our personal readiness to judge him, but the historical fact that the Sixth Ecuмenical Council anathematized Honorius by name, that Pope Leo II confirmed that judgment, and that the Eighth Ecuмenical Council explicitly reaffirmed the Sixth and repeated its list, including Honorius.

Oh, I thought the question was "heretic but pope until death? (Pope Honorius I case)".

The answer seems to be: "not at all certain that he was a heretic, quite possibly (perhaps even probably) not".

Perhaps you are making the point that these Councils considered him to be a heretic, yet he was not posthumously stripped of office.

There seems to be some merit in that argument, yet it still does not involve the Church's infallible magisterium.

Just as Pope Honorius I did not teach heresy ex cathedra, an impossibility, he remained pope until his death, despite being anathematized as a heretic by the Sixth Ecuмenical Council, confirmed by Pope Leo II, and reaffirmed by the Eighth Ecuмenical Council. The councils judged his theological error, not the legitimacy of his office. By the same principle, no earthly authority can remove a pope, and post-Vatican II popes likewise retain the papal office until death or valid resignation, even if their non-ex cathedra teachings are or were theologically erroneous propositions, opinions suspected of heresy, or opinions approaching heresy. Such teachings may also render a pope materially heretical, meaning the error exists in the teaching without imputing formal, obstinate heresy to the person. They can, however, be posthumously condemned and anathematized as heretics by a council and ratified by a pope, just as Honorius I was.