I—ve had feedback from customers that they could not cancel the class after has started — is that correct, or is that just while I—m still on my trial period?
Yes, correct. Customers can not cancel their bookings more than—0 hours before class—starting time by default.

This is setting you can change on Settings > Main Settings
Note that this setting accepts decimal numbers. Eg. 0.25 means customers cannot cancel less than 15 min before class.
Note that you can also create courses (Eg. 8 Weeks Course) where customers prepay the whole course and are automatically booked into every class in advance.
See also
How do I book students into courses manually?
How to Cancel a Booking both from Dashboard and the Client—s Widget?
How to Cancel an Upcoming Class in the Future, for Example Taking a Week Break?