"I totally understand products going obsolete and being unsupported, but I can't believe my perfectly functional piece of hardware has now been rendered completely useless!"
Believe it!
When Apple says they "no longer support Apple TV Gen 1", they really mean that they have changed iTunes to make it useless, so you'll buy a new Apple TV. iTunes simply won't recognize it. You can still play music and see your pics (at least mine worked that way, since everything is on its hard drive), but you can't use iTunes to change pics, and you can't change songs or playlists or anything.
So, I bought an ATV Gen 4. Then had to buy a new stereo receiver, since mine was over twenty years old and didn't have HDMI connector. THEN had to figure out a bunch of other stuff. It's been real educational.
And, now my new Gen 4 Apple TV has to be RESTARTED every time I turn it on to play music. It takes about five minutes to go through all that, every time I turn it on. I'm not impressed with the gen 4 Apple TV.