If no one was really interested in the Schism ongoing then why did it last more than half a century?
As said in the post you answer, it's mostly about a difficult political situation and how things went out of control, really quick.
For a bit less of forty years, France being ungulfed in an uneasy peace to quasi-civil war, the Empire knowing the joys of yet another troubled succession and inner infighting, Castille being busy with his own internal disorders,... Everyone that could have led to an earleir political resolution was simply going trough other issues for the time being.
"No one was really interested in the Schism ongoing"? Indeed, but my point is that most of the "usual suspects" (bureaucratized states, religious reformators, etc.) said to have wished it to be maintained, simply didn't benefited from it and actively tried to deal with the situation.
Does that means that not anyone tried to advance its own positions? Not really, but it's more (as I said in the post you're probably mentionning), it's more on the earlier part of the crisis, when everyone tought it would be resolved soon.
When it obviously didn't, and spiraled out of control, the situation became not only politically but institutionally REALLY problematic. Two pontifical bureaucracies, raise of religious taxes, clergy being at loss (up to the point attempting some proto-gallicanism before realizing it served no purpose), and states courts and offices being unable to really do something as long they didn't sorted out their own issue.
It lasted 40 years, because while papacy was really weakened politically and institutionally since the events of the XIVth; secular states weren't just stable enough at this point to really appear as a viable alternative : again, it was attempted and failed. Big time.
Not that having two pontifical institutions didn't allowed ambitions and to gain some political cookie points, but not so much : which kind of legitimacy can you get from an impoverished papacy with debatable legitimity itself?
Eventually, it quickly went down to the contrary of what you might have seen on several maps, depicting each country having sided with one pope : in most of the Latin Christiendom, you had diverse alliegance, in a same kingdom, county or even town. Political powers could support (rarely fully, for the aformentioned reasons) one or the another, but it could as well shrug it off (as Philippe le Bon did in Flanders), and the norm was rather a religious community not supporting as much one pope, than the idea of papacy.
Someone must have benefited from it, and that "someone" IMHO is the French kings who supported the Avignon Papacy in the first place.
You confuse "someone must have benefited" and "people had interest having this situation going on".
As for France as the usual suspect, you're confusing (and that's a real historical issue there) the French policy to Rome/Avignon in the larger part of XIVth, which was not too dissimilar to what HRE tried to do in its time; and the Great Schism.
Basically, the second is tied to the first, in the manner that the cardinal and pontifical bureaucracy issued from Avignon Papacy was less prone to accept the usual not-that-valid Roman election model (usually involving mob gathering) and even less Urban IV temptative to curb down their power.
But there, we have to point some facts, and not just opinions.
The election of Urban IV was initially supported by Charles V who didn't played any role into the political/diplomatical shenanigans, at the contrary of Naples. Certainly, he did accepted the situation (less for obvious political benefits, than support of french cardinals), but to see Valois' hand as the cause of the schism is nothing short of conspirationist.
Until 1388, Charles VI's regency is essentially busy with inner matters, not only not really giving support to anyone but even (as Philippe did) shrugging it off, doesn't strikes me as "benefitting" from the chaotic situation. Except assuming they'd did it for shit and giggles.
In early 1390's, Charles VI was so benefitting from the schism ongoing, that the only thing that prevented him to launch his planned expedition in Italy to crush Roman papacy was that Richard II pointed that it would see it as breaking the de facto truce between them. (Gian Galeazzo Visconti tried to salvage the project, but died quickly, with his Italian hegemony crumbling down).
In the late 1390's, the regency of Charles VI changes from policy, and favours a negociation on mending the schism (the boldest support of Avignon, as Louis d'Orléans, are eventually put apart) : it fails because both of the popes refuse to abdicate, which led to the ill-fated soustraction d'obédience in France (and French allies).
In facts, and not opinions, the benefit from the Schism (or ongoing schism) seems at best meager, giving it not only institutionalized previous political issues, but created anothers.
TL;DR : Did Valois, and other princes, had interest on supporting one or the other pope? Yes, altough it's far from systematicaL
Did they had interest seeing it continuing much longer? Nope.
my understanding of the matter is that the German princes and merchants threw their support behind Luther because he offered a more localized church subordinate to the secular interest, and exploiting feelings of German disdain for Rome "exploiting" them and taking the tax money
The purely materialistic and economical explanation generally fails at explaining the situation completly.
The first explanation is the capacity of Lutherianism to answer the spiritual questioning of the time : which was far less based on the weakening of papacy (if anything, it blamed the too important interventionism of Rome), than the more individual and less institutionalized spiritualities, such as the devotio moderna.
The sheer weight of late medieval/early Renaissance Papacy (less popes themselves than the whole of institutions) prevented to make a real aggiornamento about this (it did eventually at Trento, but not before it went really out of control) : Lutherianism simply was more fit to answer these questions.
The idea that the Catholic church should be reformed was omni-present in the XVth, even if most of it doesn't get as disruptive as Hussits or Lollards, and the ongoing gap between this precieved necessity of reformation within the Church, and the lack of significant effects pushed to distanciation (humanist, proto-gallican, etc. including, of course, Lutherianism)
Again, the first cause is moral and spiritual.
Now, why didn't it get imposed elsewhere than Germany in Europe?
After all, if it's all about secular interest, you should see it happening in France, Netherlands or even Italy.
And if it's just spiritual, it should have been apparent in Spain, Protugal or even in the southern part of the Empire.
The political situation in Germany was particularily complex, at best.
Political and dynastical relations played importantly : nobiliar conversions were usually made along familial links.
One could disagree a lot with Roman church, but when your interests were much tied with imperial power and your alliance with, not switching "politically" was probably a sound move, that didn't said anything about your spiritual opinion (as it more or less happened with Renaissance Habsburgs which weren't exactly thrilled by the piss-poor spirituality renewal of Rome).
You can see that
Lutherans states were usually the most distant or opposed with Habsburgs, eventually.
Let's not forget, evetually, that the rooting of Lutherianism, but also Reformation as a whole, was extremely depending on secular protection and dominance : if you had a Lutheran prince, you probably saw more Lutheran population, even if it doesn't fit the comically flawed Weberian economist model.
Did you had a disdain for Rome? You had, but less because it was weakened, than because it was relatively strong after a bad XIVth century : but again, it did appeared elsewhere (there was nothing that much specific to German proto-nationalism on this regard) than Germany.
and also that the advent of printing helped perpetuated heretical doctrine more rapidly and uncontrollably than say the Hussites.
Only partially : a good part of the reformation touched illetrate or quasi-illetrate population on a scale not seen for most of medieval heresies. Let's be careful not seeing printing press as some sort of magical device there,
especially giving that Northern Germany wasn't that well equipped on this regard, at least compared to the rest of western Europe.
Prior heretical sects- the Cathars and Hussites being the two that come to mind- were largely "nationalist" in the sense that they were tied up in a sense of regional defiance and particularlism in contravention to a centralizing imperial authority
Unfortunatly, it happens that I know relatively well the question of medieval heresies as Catharism.
I won't go too much into details, only to say there's no, as in zero, nada, que dalle, historical sources that could support a proto-nationalistic analysis. It generally go down to an half-digested version of religious life in middle-ages, which fails to take in account that it was widespread in most of continental Europe, and lived down longer in certain regions due to political reasons (such as complex and divided polities). I'm still to see ONE good argument into making it a proto-occitanism.
Contrary to Hussism, for instance, it's generally fairly absent from countryside, and relatively present in urban centers (mayb 10% in towns like Albi, but it fall down quickly as soon you reach Lower Languedoc or Gascony) or peripherised nobles, and while civic/dynastical solidarities played regularily, it was far too cornered geographically and socially to really be claimed being a regional heresy, in the sense it provided something of a regional identity.
As for Hussism.
I think it's failure was less that it was proto-national (while it was certainly more than any medieval heresy one could quote, which is admttedly not hard), that being too radical politically and religiously, as was Lollardism; which eventually led to Taborite/Hussite infighting (to not mention adamistes). Eventually, it was a redux of the Peasant Wars on some respect, and the unability to win over secular princes (urban or nobles) in a significant manner did buried it out.
Not that proto-nationalism didn't played a role there, but I don't think it played the major role or was close to do so : there's room for argument on this, I suppose, tough.
and Lutheran (and other Protestant strains) mirrored this, being more successful and widespread in the German states.
Lutherianism and Hussism have clearly more ties than any of them with other medieval heresies, with the aformentioned caveat that Hussism inner disputes and radicalism was a real hinderance, when Lutherianism managed to remain in one part (If Luther had died the same way Hus did, it might have been different) managing to not radicalize itself too much socially (altough the Peasant War certainly did its job to prevent a lot of German princes and towns to switch it over to Lutherianism).