Maybe you could get a friend to ring your vet on the pretence of asking for an appointment, and see what choices they give on that day. If it sounds like there are lots of appointment times available, it could be further proof that they're not busy and looking for business.

We take our cats in once a year for checkups and vaccinations, and buy a year's worth of worming and flea treatment at the same time. No need to take them back unless we think there's something wrong. I think elderly or other kitties with ongoing health issues should go more often, but otherwise, I think it's unnecessary to go in for the sake of it ... FWIW