I thought it does—we rented a movie with Apple TV at one point a couple years ago and waited for it do download to local storage before it was played. Unfortunately, I had opted for highest quality at a time when our network connection was being really flaky and it took a day to do so.
Maybe certain streaming services allow you to download as well though their app on the Apple TV, but most of the big ones don’t (Apple, Netflix, HBO, etc.)
I really don’t like it because, besides wanting to pre-download something for higher quality, there are often certain shows and movies my kids want to watch over and over and they might as well just live on the hard drive.
So I have a 64GB Apple TV and most of the storage is empty. Theoretically it’s for games, but ATV games are limited to 100MB and then anything else has to be downloaded after the game has installed. (In practice there aren’t any games near that big). I suppose device might also progressively download the video in the background and that would use storage, but that’s all an implementation detail and entirely up to the heuristics of the device.
Ooh, I hadn't thought about the streaming services. I was really annoyed to discover that a movie I'd downloaded to my iPad from Disney+ would not play if the iPad was connected to a TV which was damned obnoxious. This was a rental from the Apple TV store and not an Apple+ stream, so maybe that's where the difference comes in.
