Serenity Caldwell, writing for iMore:

When you try to sync offline Apple Music tracks to a nano or shuffle, you’re met with this rather disappointing message: “Apple Music songs cannot be copied to an iPod.” You’ll have to rely on your purchased music for those devices, instead.

As to why, Serenity speculates:

It’s probably a record label requirement: In theory, you could sync an iPod shuffle or nano up with Apple Music tracks, then cancel your Apple Music subscription and continue rocking out to those “copied” tracks forever.

Homing in on this a bit, I think the issue is a lack of a keyboard, the lack of an ability to log in to your iCloud account, the lack of accountability.

As Kirk McElhearn pointed out in this post:

Since the DRM on the files links to a time-limited account, you can’t copy them to a device that can’t check if your subscription is still active.

I’ve got no issue with the incompatibility between the nano/shuffle and Apple Music. It is what it is. That said, I do think this ranks up there with the smaller footprint iPhone as an issue that the consumer should be made aware of when they click the Buy button.