"Apple can still make it work, especially on the latest iPod nano."
How do you know? Are you a current/former Apple developer, or have detailed insight into the nano's firmware code and operations?
"They can require nano to be connected to iTunes every 30 days to verify that subscription is still active."
So you know that licensing and other legal agreements between Apple, media providers, and artists include provisions covering a subscription verification method that is very different from that used by all devices that currently support Apple Music?
"Maybe that would require firmware update but it seems feasible."
Feasible, possibly, but is it economically worthwhile for Apple? Do you suppose that Apple haven't done marketing studies and demographic analyses to determine the ROI on providing Apple Music on legacy iPods?