If they're AF/GF breakers, that's "probably" for a reason. You'd have to check local codes and see if it's required for a given circuit (if you're subject to modern codes, they're required in lots of places). If it is required, you'd have to put GFCI outlets in, and you'd maybe have to switch your main breaker out for an AF one? (Not cheap!)

I'd look long and hard at the actual charging rate you need. 60A is big and could push the load calculation for your panel over it's limit, especially if you've got a big AC or anything like that. Have you done a load calculation (you better, if you're adding a 60A load)?

Most people charge their cars overnight, and even 20-30A (at 240V) is more than plenty for that, even doing large amounts of driving per day.