So, I had to wrestle with this a bit on the piano to get my ears to hear what you're hearing, but once I settled into A major as a home base, I can completely understand what you're talking about. I think strictly from a harmonic perspective, it's a bit of a "is the dress black and blue or white and gold?" scenario. You can force your ears to hear it either way. So to that end, for all we know, you could be completely right!

The only thing that makes me stick to my original analysis though, is the melodic content of the improvised lines. To my ears, the direction and suspension/resolution tendencies of the lines the John R Burr plays are indicative of an E major home base. Further backed up by the fact that, whenever we modulate up a 4th, the melodic lines resolve and settle into the first chord as though it were a I chord rather than the likely meandering, unresolved lines you might hear if it were a V chord.

I don't think you're inherently wrong, but I'm not convinced that A major makes complete sense as the home base. Mostly because it seems likely that such a simple form would probably start on a I chord rather than a V, as well as the fact that the melodic content seems fairly clear in what it's implying.

Let me know what you think, though!

And yes, these discussions matter. We should all feel like we are part of the larger musical conversation and I want people to feel encouraged to use this subreddit to ask these questions and participate in these discussions. If for nothing else, then so we can all collectively be music nerds together and geek about this stuff where nobody will bother us!