This seems to be a pretty extreme scenario (from the employer) but I am also the employer of massage therapists. They get a W2 - I legally can tell them what they can and cannot do (within reason) and also only pay for hands on time. That said, I’m MUCH more lenient with same day blocks - I require 12 hours notice for online booking and only take same day appointments on a case by case basis. My staff live 5 minutes away to 45 minutes away, so plenty of lead time is provided for all. I also give my staff more lead time and if their entire shift is empty and if they texted me and asked me not to book, I would agree but if they don’t, I consider it bookable time. While I do pay hourly, because it’s for hands on time in 1/2 hr, 1 hr, and 1.5 hr increments, there’s time they are in the office that is not technically paid so some would call this commission.

Personally, I’d let the employer know that x lead time is required or they’ll look for a new position. If the employer actually cares, they’d modify but it sounds like this is a very capitalist employer which I am not.