If you have async stuff happening all over the place, what do you use, a global ThreadPoolExecutor? It's not bad, but a bit more cumbersome and probably less efficient. You're running multiple OS threads that are locking, vs a single-threaded event loop. Gets worse the more long-running blocking calls there are.
Also, I was originally asking about free threads. GIL isn't a problem if you're just waiting on I/O. If you want to compute on multiple cores at once, there's multiprocessing, or more likely you're using stuff like numpy that uses C threads anyway.