As you know, a bishop holds a Crozier, which is like a shepherd's staff.
He is the one ultimately responsible for his flock, although necessity dictates that he delegate much of the daily work to the priests under him. That leaves the bishop's role primarily one of LEADERSHIP and PURITY OF DOCTRINE.
If his flock veers off towards the right, (for example, Jansenism) he will remind them of the Sacred Heart of Jesus, God's mercy, and will correct their incipient errors.
If his flock veers off towards the left, (for example, the Novus Ordo) he will remind them of the unchanging nature of Tradition, the rights of God, the errors of Modernism, etc.
In all things, he strives to keep the flock on the narrow path. This necessarily involves purity of Catholic doctrine. After all, doctrine can be corrupted either by EXCESS or DEFECT -- deviating to the RIGHT or the LEFT.
There are two main ways of corrupting any doctrine or morality: excess and defect.
Exaggerating the humanity of Our Lord would be as spiritually fatal as minimizing it. Every heresy is either an exaggeration or a minimization of a CATHOLIC TRUTH.
A bishop must strive to maintain the purity of Catholic doctrine within his diocese. He must "pass on what he has received" or he will have to answer to the Strict Judge. This also involves making sure that not only his Faithful are doing the right thing, but that they are doing it for the right reasons! If his Faithful are all fasting, because they believe the End of the World is next Thursday, he would get involved -- on principle -- to correct them.
Likewise, if a group of Catholics were attending the Tridentine Mass, but only because they believed that "one must attend the closest Mass to one's house" he would have to correct them.
A bishop doesn't have "it's all good" in his vocabulary. It might be seemingly good for these 10 people over here to faithfully attend the Tridentine Mass. But what if they labor under objective errors about the Novus Ordo? Shouldn't he correct them?
An ignorant laymen might shout, "No!". Nevertheless, that layman would be wrong. The bishop, being wise, knows that eventually those errors will come back to bite those 10 apparently faithful Traditional Catholics. Error is NEVER your friend, even if it convinces you (for now) to do something good. Tomorrow, it might lead you in a completely different -- and much more evil -- direction. Principles and truth are of the utmost importance, and any wise man understands this.
Isn't PRESERVING AND PROMOTING THE TRUTH the main job of a Catholic bishop?
Witness the recent problems in the SSPX: so many Catholics attending the SSPX Masses every Sunday -- they were all apparently good, solid "SSPXers" but just look at the variety that was there. Look at how many weren't there for the right reasons. Look at how many DID NOT UNDERSTAND THE ARCHBISHOP AT ALL. Look at how many were actually left-leaning Indulters in disguise -- or right-leaning cultists (*cough* Pfeifferites *cough*)
As soon as the tree was shook, look how many apples fell to the ground. All was not healthy in the SSPX pews.