but it would be quite possible that a few more years (and a more stable state) might change his mind.
The stabilty of a late feudal state isn't really function of its transmission. GG would have to deal with the same issues than similar "border states", such as Burgundy later, meaning many distinct identities to deal with, trying to compromise between an idealized feudal mindset (even if I agree heartily that it wouldn't be at the same scale than Burgundy in its time)and dynastic necessities.
As I tried to point, I don't think having a succession crisis after his death would be a bad thing
on the long run : it would force the apparition of a more "updated" and precise conception of political inheritency. At the cost maybe of part of GG's conquests, that said.
The Great Western Schism lasted for 70 years. It does not look to me that it was such a huge problem for the political powers, much less for the common people. It might have gone on for another 70 years, and maybe after such a time the need for a pope might have been no more there.
It lasted for 39 years. 1378-1417. You may have added the Avignon Papacy, that is a distinct feature.
If something, the number of unsuccessful attempts to resolve it, and the fact they still tried to make it during this period, should point out that yes, it was a thing.
As for the common people, in a time where religion was a really important identitary factor? Yes, it played quite well, especially in urban settings (due to the clerical, in the non-social meaning, presence).
It doesn't mean that heterodoxial practices doesn't emerge face to the crisis, but it was one more factor motivating secular powers to try resolve the crisis themselves (Heresies were often a destabilizing factors, and almost always attacking the power in place. For exemple Lollards attacked heavily the late feudal system, something that rulers couldn't really accept)
OTOH the counciliarist movement is quite active between the late 14th and the early 15th centuries, and Wycliffe and Hus are preaching in these years too. The 15th century is a time of great changes.
And again, Conciliarist movement
never was about removing the pope or even limiting its powers. These councils were essentially representative of high clergy and nobility, whom legitimacy depended from pontifical hegemony and coudln't have touched to this without having a huge backfire.
Their main goal was being some sort of collaborating weight, critically when it came to everyday administration. They weren't that much different from the late feudal ideology that argued that the kings and princes should live from the revenues of their lands and not use taxes that were supposed to be exceptionnal.
Basically a tendency going against the formation of modern administrations and bureaucraties, praised by a body that wanted to be part of this bureaucracy.