TVs are optimized for living room viewing, with (better) build-in audio options (and passthrough options), multiple HDMI inputs, new screen technologies (e.g. OLED and Dolby Vision), larger size availability, better contract (e.g. through local dimming).
Monitors are optimized for close distance viewing, with more PC-oriented input options, low lag, more refresh rate options (including many that do not apply to TV show or movie content). Monitors that are not 16:9 aspect ratio will not be optimized for use with Apple TV (or similar media players).
The Apple TV box will adapt to the capabilities of the screen either way, as best as it can. Depending on monitor audio options and your intended audio system, you may need to route the audio separately, which may involve an external Audio Extractor box.
Set up your Apple TV - Apple Support