TIL that an iOS device has to have at least one local music file synced before it will display the dropdown menu that lets you choose to listen to an iTunes Home Sharing library

It was driving me crazy that I couldn't figure out how, in the newer "Music" app on our phones or our iPad, to listen to the iTunes library that's shared from the Mac Mini in our house. I'd be at home, I'd connect to our wi-fi, I'd make sure everything was correct on the Mini, and I'd verify all the iOS settings had my Apple ID identified under Music for Home Sharing...but I could never find this drop down menu all the documentation and examples seemed to have. I finally realized that due to poor UX assumptions, you can't ever see that dropdown while the "hey, you should put some music on this device" screen (paraphrased) is active. You have to put at least one song on the device, so that screen goes away, before you can possibly choose to listen to Home Sharing.

Thought I would share this in case someone else out there has the same use case and confusion...I have no desire to have any local music on my devices, but the assumption is so strong among Apple's developers I guess that you've just gotta have a little bit on there if you want to be able to stream the rest of your own stuff across your LAN.