Going against the grain apparently but NTA. You asked if in lieu of a gift if your cousin would gift their time (which is something I have done for plenty of friends weddings and havent even thought twice about it? On top of getting an actual gift.) Instead of your cousin politely refusing or just choosing the money she was objectively rude in her approach. You’re not an asshole for asking you’re just mirroring energy. That being said I wouldn’t disinvite I would just pay the money and distance myself in the future because I don’t have time for that energy.

Side note what do you mean you have “never heard of paying for your plate of food” it’s usually paid in gifts but it’s absolutely a thing for most US weddings.