Is it legal for a doctor to charge a late charge on a no show appointment?

Unfortunately, it is legal for a doctor to charge someone for an appointment even if they didn't show. This is because the missed appointment takes time and money away from the firm.

Time: because they have to make follow up calls and reschedule the appointment.

And Money: because they could have had another patient during your missed appointment.

Since it has become common for people to miss their appointments it has become more common for doctors to charge anyway.

You should reschedule the appointment a few days beforehand to give them time to find another patient for the alloted time.