(By the way: most of the time, a plain-old-boring thread-per-request is just fine, because most of the time, you're not writing high-scale software. If you have at most two dozen concurrent tasks, you're wasting your time worrying about the overhead of plain old pthread_t.)
I'm using a much more expansive definition of "thread" than you are. Sure, in the right situation, maybe M:N threading, or full green threads, or whatever is the right implementation strategy. There's no reason that green threading has to involve the use of explicit "async" and "await" keywords, and it's these keywords that I consider silly.