Enforcing DRM is expensive. If it was up to Apple, there would be no DRM. The content producers specify the requirements for Apple Music's DRM, and Apple implements it. Apple's motivation is to sell hardware and minimize service restrictions that hinder sales. The content producer's motivation is to maximize subscription-based revenue while minimizing piracy through restrictions. Apple Music exists as a compromise between those two opposing goals, and it apparently does not include support for iPods, except for iPod touch.
iPod touch is a great device, amazingly thin and light (especially compared to current "big" iPhones). I have an iPod nano that I use for running, but I also have an iPod touch (5th gen) that I use to watch Netflix, Hulu, and YouTube, and to stream Apple Music. For me, it's the ideal all-purpose hand-held media player. Big enough to watch (and enjoy) videos comfortably. Small and light enough to carry around easily for audio streaming.