Actually, you cannot sync Apple Music to an iPod at all. You can download it to an iPod Touch over wifi, but you can't sync Apple Music to it from iTunes. And you can't sync Apple Music to an iPod nano or shuffle or other iPod at all.
This is why I will let Apple Music lapse in 2 1/2 months.
Same here. I use my very old 30GB iPod via USB in my vehicle for music. Sometimes I use bluetooth with my iPhone 6 and stream Apple Music... and even though it auto-plays at times picking right back up where I left off before if I want to switch songs I have to navigate Apple Music till I find a playlist I like. That doesn't take very long, but my built-in navigation for my iPod is pretty easy with a few clicks on my wheel to grab the playlist I want.
But you raise a very good point about letting Apple Music lapse if I can't download some music to my iPod (even if there was a requirement to check back in or have the music expire after a certain time I'd be fine with that to keep my old gear).
Also, I don't always get cell data service when I'm driving out of town so I can't rely on Apple Music solely.