The other kind of gym keeps membership to a fixed number, and will actually drop you as a member if you don't follow through on commitments to visit regularly, exercise, and get fit.
You can guess that the former business model is much more common than the latter. And obviously they cater to different segments of the market.
Compare gyms to your idea. Which model do you prefer? Oversell real estate? Or gamify people into chasing an artificially scarce resource?
This is a cynical take. But it's going to take marketing for your idea to succeed, and marketing is fundamentally about getting people to do something they don't want to do.