I’ve never been a coordinator, but I have taught group ex in a fairly wide variety of settings, and I’ve run my own program. It is common (I wouldn’t say universal, as there are always outliers) to track class participation. Some places don’t seem to tweak the schedule on a regular basis, unless there is something new they want to add, some revamp the schedule at a more regular basis. I’ve been places where a class or instructor will be moved to a different slot. I would say that is more common unless the instructor is problematic for other reasons, such as the one you mention (extreme tardiness). I have seen it happen where a slow class/instructor really grows if it is placed where it will reach the right audience. It is kind of like before everyone had VCRs and they would schedule a new show opposite a really popular one.
This by the way is one of the things that really matters in hiring a coordinator. A coordinator that only teaches one format will understand that one well, but might not really get the balance of all the options. Most of the best coordinators I’ve known teach at least 2 formats, and take the time to get to know members who are not in those classes, and to take other classes.
Of course, sometimes a class that is popular might get cancelled for other reasons….. such as the center buying a trademarked program and needing space to promote it.
I certainly know of instructors who have lost classes for repeat tardiness. I have also taught where the management did not set great standards themselves.
I think it is good to have a policy in place and to hold people accountable. I taught a5 am class for years and only missed it twice… once when both of my alarms failed, and once when I was (literally) up all night bailing water out of my basement and it was still flooding when 4 am came. At that studio missing last minute once was forgiven, the second time I taught the next class for free to make up. That seemed like a fair policy to me. It really makes you want to save your ‘get out of jail free’ card till you really need it. 10 tardies seems like too much. The professionalism of your center will be judged and found wanting even if the instructor is good. It might be useful to have a tiered system, where they are given a warning at a defined time, and where it is in writing and read and signed by both parties what the expectations are.