You can look at all that stuff and start drawing all sorts of conclusions and many of them might well be wide of the mark. What's not in doubt, however, is the fact that the sessions brought together many of the elements that resulted in Music From Big Pink, and that's where (at least in my opinion) the influence on what came afterwards really starts to kick in.
For a start, under other circumstances the sessions might never have happened at all. One guesses that The Band were being paid a retainer to keep them on hand so that when Dylan resumed touring they'd resume the backing band role. Dylan, arguably had no such intention, and had Albert Grossman been aware of that there's every possibility that he'd have been saying sorry boys, back on the road.
It's quite likely the sessions were presented as evidence of an intention to resume touring at some unspecified point in time and a justification for keeping those retainer payments rolling in.
What is more important the sessions put Robbie Robertson, Levon Helm and confreres in touch with a body of material they wouldn't have been likely to come across otherwise.
For Robertson, the street kid from Toronto who may well have ended up in prison if he hadn't started playing guitar, his dealings with Dylan resulted in all sorts of influences that subsequently came out in his song-writing. To Levon Helm, on the other hand, some of those elements would have been reminders of where he came from, pointers to a possible future direction, and you'd expect there were similar reactions from Messrs Danko, Manuel and Hudson.
More significantly, the Publishers' Demo provided the framework around which The Band assembled what became Music From Big Pink. That's not to downplay the original material on the album, but one suspects that they didn't have a whole lot of material to choose from. Three of the eleven tracks (Tears of Rage, This Wheel’s On Fire and I Shall Be Released) come from the Basement, and there's also the cover of Long Black Veil. The bonus tracks on the 2000 remaster include a couple of other Basement tracks, and, most significantly, the best known song on the whole album, The Weight, was recorded as an afterthought when they didn't have quite enough material to fill up the album.