If you want to be in a band, you need a PA - so digging one’s heels in and saying ‘I’m not paying’ is unlikely to prove worthwhile or popular.
However in this situation it’s different, with an already (presumably) decent PA that doesn’t need an upgrade. I’d be happy putting it to a band vote and if it’s deemed unnecessary then it doesn’t get bought.
I’m always bemused by the pickles that some get into with shares of PA’s, and I own this and you own that, and you can buy me out etc etc.
A PA, once bought (by band earnings ideally) is a sunk cost. Write it off.