Browser fingerprinting is a thing (identifying someone by their browser's configuration and fonts, amongst other things), but I don't see them using that for bans honestly.
For what it's worth, having a few "bigger" instances means less confusion for users who don't completely understand federation yet but still want to make the switch. I wouldn't call it a bad thing, they can always turn to another smaller instance later on.
Apologies for the self promo, just trying to get it started. Feel free to delete if this isn't allowed :)
A ban for first offense seems excessive, but to be fair, this whole situation must be quite stressful for them and being asked by hundreds of users for support of X or Y alternative seems like it would quickly become annoying.
Note that a lot of free VPNs are easily identifiable and blacklisted by a lot of websites. Hell, even some paid ones have blacklisted IPs sometimes.