Not quite what I was getting at. The formula of Hormisdas and the Henotikon were both failures because the former demanded that Chalcedon be accepted uncritically, while the latter marginalized Chalcedon completely, instead only demanding that bishops profess faith in the twelve chapters of Cyril and that they uphold the condemnations of Eutyches and Nestorius. It was only at the Second Council of Constantinople where Orthodox Christology was properly set forth (most importantly the council’s recognition that the two natures are perceptible only in contemplation, and that the formula ‘of two natures’ is orthodox, so long as it is understood that the natures do not mingle or become confused; without these important clarifications, Chalcedon could have possibly been interpreted in a Nestorian manner). This was, at its heart not a matter of trying to reconcile with the miaphysites, but an attempt to define what the Orthodox faith was, because Chalcedon was not sufficiently clear as to what ‘in two natures’ meant.
The pope was effectively deposed, considering that he was exiled, only being allowed to return to Rome on the condition that he approve of Second Constantinople. It might have been out of concern that such an action would not have been supported by the Romans that no deposition took place. When we see patriarchs being deposed, they are of course within Imperial territory, such that the deposition could be enforced by the state. Because of the Empire’s weak hold over Rome, such an action would have been pointless, because it would have been impossible to enforce.
It is no mistake, for example, that the miaphysite Churches survived in Egypt, Africa, and the Levant, because the most the civic authorities could do without causing rebellion would be to install their own Chalcedonian bishops. The empire probably did not even have the power to install its own bishop in Rome, much less depose him without the consent of his people.
By your logic, the bishops of the see of Seleucia-Ctesiphon were also impossible to depose, because nobody deposed them once they accepted Nestorianism.