I'm pretty sure you can harm your credit and have the debt get sent to collections by doing this, at least it's common for gym subscribers not paying their fees.
Good point. Fortunately, where I live, subscription fees are typically charged before the next billing period begins, so there usually isn't any outstanding balance carried over. Credit-building in the North American sense also isn't much of a thing here. My understanding is that, even in North America, most of the benefit comes from just consistently paying your credit card bill, although I can't say that with certainty.