The schedule is the most-visited page you have
Existing members check the timetable constantly, and prospective members use it to work out whether the gym fits their life.
For members it is a utility they open several times a week, usually on a phone, often in a hurry. It should load instantly and be readable without pinching.
For prospects it answers the deciding question, which is whether there is something at a time they can actually attend. A gym with nothing at seven in the morning is not an option for somebody who trains before work.
Schedules delivered as a downloadable file or an embedded widget fail both. The file is unusable on a phone and the widget is frequently slow, and neither can be found in a search for a specific class at a specific hour.
Real page content solves it. Class names, times, what each one involves and who it suits, as text a search engine and a screen reader can both handle.
Accuracy is the other half. A timetable showing a class that no longer runs produces a member arriving to an empty room, which is worse than a plain page.