But more to the point-- regarding unity-- I see you are backpedaling from your initial claim that the office of the pope unites Catholics.
I'm not backpedaling. The papal office is a unifying symbol because it represents the link to Apostolic times and the consistancy throughout the ages of doctrinal teaching and the reiteration of Divine Law. A specific pope is only unifying because he discharges the office. If the office is empty, then unity will eventually vanish. The Church is only legitimate because her doctrines are unchanging, which is only possible with the protection of infallibility, which is not promised to a person, but to one who excercises the papal office. A bad pope does not exercise the full papal office but only the material aspect since his spiritual capabilities are impaired through his own fault.
the pope is the principle of faith (and unity) because in this person... there are certain providential protections afforded which guarantee, a priori, the impossibility of certain errors.
Right, infallibility protects against error, when it's used. Aside from this, in all other fallible matters, the pope can err. There is no Church teaching which says that the pope is protected from error outside of infallibility. At best, some theolgians argued his personal faith could not fail. But many others argued that it could, including +Bellarmine.
That makes unity with him unity with Christ, and especially an assurance that one has the correct doctrine when one learns from him and obeys his laws.
This is an exaggeration of the pope's orthodoxy. If it were true, then the 4 requirements for infallibility would not need to exist because the pope would, according to your understanding, be infallible 100% of the time. Yet theologians have explained in great detail there are MULTIPLE levels of Church teaching, some infallible, some totally fallible and others in between. It's not as simple as "Well, the pope said it, so I have to follow." He can't say or command anything he wants.
In orthodox times, the Cardinals and Bishops would be the buffer between a quasi-heretic pope and the laity. They would be the first to read encyclicals and bulls and other such official docuмents and if there were departures from orthodoxy then they would challenge/question the pope on it. It's only in modern times (last 80s years) that is was even POSSIBLE for the pope to communicate with laity directly (since the invention of the radio). Before that, he issued docuмents and it flowed from him down to bishops, then to priests, then to the laity. So the laity was not necessarily hearing directly from the pope, but from their bishop and priests, whom they would trust, rightly so. And these bishops and priests, all over the world, would be the "checks and balances" in the system, if any were needed, to appeal to rome for further answers. But V2 was an infiltration where the bishops/priests were agents waiting to get the agenda from Paul VI and install the new program for the new religion. The normal "checks and balances" were neutralized.
So the reality of traditional Catholicism today-- which is a very divisive reality-- is perfectly consistent with what one would expect in the absence of a pope.
Practically speaking, a bad pope is the same as no pope. Division happens with there is either bad leadership or none.
You can criticize it for having no solutions but it isn't supposed to be a solution, and any sedevacantist who thinks otherwise should take a step back. It's simply a description of the problem, and in my opinion an accurate one.
I don't criticize sedevacantism for its theory or goals, which are good (i.e. keep the Faith). I criticize, very specifically, Fr Cekada's spirit of division in the "una cuм" controversy where he takes a theory and attempts to compel and coerce people to attend sede-only masses under the false and doctrinally-ridiculous idea that to say the pope's name in the canon is to be complicit in every heresy of the day, and consequently, to be in grave sin. This is not the purpose of the prayer and i've seen first hand the splits in families, the turmoils, the divorces and other consternation which has resulted from the false and extreme zeal that people have for this "una cuм" lie. By their fruits you shall know them and there are NO good fruits from the self-imposed, self-serving and self-authoritarian Cekada-doctrine of "una cuм".
If sedes would stop this particular nonsense, then i'd have no problem with them. As it is, they create enemies where there need be none (i.e. other Trads).