I've got a couple of Coway HEPA purifiers, and they can be quiet enough for a classroom. At low speeds, the closest to inaudible that I've ever heard, and at higher speeds a very even and tolerable white/brown noise.
I'm sure some that are good-enough and not loud exist, and some classrooms probably have them, but I can also say for a fact that some schools that have managed to get ahold of good purifiers for every classroom haven't also managed to get ahold of quiet good purifiers, which is why those schools only run them part of the time. It's another hurdle to the solution of "just filter the air", which isn't per se a bad idea—but, whoever's procuring them must think to look into the noise when choosing which to buy, must have the budget to buy quiet ones that move as much air as appropriately-effective louder models (I assume there's a cost premium for "quiet and also effective"), and if someone's already bought purifiers and they're too loud, you're out of luck on getting anyone to pony up cash for a second set of (maybe even more expensive) purifiers.
They can be too loud to run while class is in session, especially if they move enough air to be worth a damn. Double-especially if you're also masked (so speaking is already a bit muffled).