I agree there could be a million reasons for it; but I think you hit the nail on the head in the first part of that paragraph. Everything that's been done live since the tour ended has been Jon. By himself. And tbh, as far as Jovi is concerned, Jon seems to be the only one who cares about doing anything live or promoting anything related to the new album.

Jon seems to be trying hard to maintain a presence in the media, especially since the pandemic started and it became clear the album and tour would be delayed. He's been doing that himself; but to counteract the negative feedback about how Jon-centric it's all become, he may have felt pressure to start including the band more. Or maybe The Voice was only interested in a full band performance. Unfortunately, it seems like the hired guns couldn't care less.

I don't know jack about what's involved in putting together something like this; but as to why Jon's vocal is live and the guys are miming a studio track, my first guess would be it's because, based on comments from Jon and Phil-X, it's been Jon's project from the git and there hasn't been a lot of input from the rest of them to start with. Maybe the band sees little point in going to the trouble of recording something "live" that Jon may or may not approve of, since he doesn't seem to want anything other than what he and Shanks have already decided on, anyway. If they're just going to duplicate tracks that were laid down by Shanks originally, why bother; when they could just act like they're playing.

Just my $0.02.