The main problem with AppleTv is no native app for the Tablo on it (due to Apple restrictions). You can definitely stream your iPhone and iPad Tablo app to the AppleTv, but that is an added step. I would much rather have a Roku or FireTv that is independent of other devices and has it’s own app.
I also had a bad experience the one time time I did use AppleTv. I used my iPad via Tablo Connect to stream to my friend’s AppleTv. It would disconnect from the TV every few minutes, and I would have to kick it off again. But I think that was more because of Tablo Connect, so it might work fine on your home network.