I think you're worrying for nothing. At first, I also watched on my phone, and that was enough for me. However, when I switched to a bigger screen with Apple TV, the movies were much brighter and more immersive. You can see what's available and how everything looks on different devices at
https://tv.apple.com/. Even if you're watching on your phone, the quality and visual effects are still very good. In particular, I also watch on my phone when I'm on the road and don't see a problem with that. As an option, you can try connecting your account to a TV or monitor to see the difference.