Yeah, agreed. I share those concerns. I'd (personally) be against having any extra features for donors for just that reason, it would create a two tier system that could get cliquey.
On the funding issue though, the main problem is that the admin always has to pay the server bill, but most active users never donate anything, so even if badges just encouraged more minimum donations it would achieve something significant.
This situation is caused by Facebook, Twitter etc implying that people don't have to pay for social media, but they do that through ads and surveillance and privacy violations. No one wants Fedi to end up like this, so it would be good to get more people aware that someone is paying their server bills, which badges might help with.
I guess in a way, this is up to each instance's own admin to decide, though? As long as features are flexible and optional, it would be up to each admin to use them in a responsible way?