.
It seems to me there would be some sedes who would find reasons to reject even a good pope in the future, but there would be some sedes who would accept him. It's not really fair to presume they'll all react in the same way.
.
Actually Neil, by definition, the dogmatic sedes of the world can never accept any pope, not even a good pope.
I can say this because I have questioned them in the past on this very subject - and the one or two that actually answered (sedes are notorious for ignoring questions) testified that no matter what, the newly elected pope would need to be scrutinized by them before having any chance whatsoever of being accepted as pope by them. As they explained it, there is no other choice, this is the way of all the sedes because it must be the way of all sedes. So based on that, it is safe to presume they'll all react in the same way which means by that very fact, they will never have a pope.
Consider to begin with, all the cardinals are heretics, therefore they have no cardinals to elect a pope. All the conciliar bishops are heretics so they're out. All the conciliar priests are heretics so they're out. They will spend who knows how long to agree on which trad bishops are worthy of electing a pope so that avenue is out. Who will elect a pope? Who will assign a pope? It won't be God, He already did that during His first coming, the next time He comes will be as Judge, so He's out.
So how will the sedes get a pope they can all agree is a true pope doggone it? The answer is, it will never happen for the sedes, never - for the reasons stated above. But the matter will keep them wholly occupied and concerned with, that's all that really matters to them anyway.