Sure could, but then you would need to do the thing AND think about doing the triggering and then find the trigger button on your watch. This way you wouldn't have to think about it, because it's automated. Triggering something manually also doesn't really count as 'automation' I would say.

Obviously not, but there is larger potential than that. A microphone in a watch or phone can pick up the signal and relay the trigger to another server via for example MQTT. Then, you can have homeassistant act upon this signal.

The flow is then Open door --> Signal triggers --> Signal caught by microphone --> Microphone device relays to server --> Server turns on smart lighting in that room.

There is a lot more that you can do, but this is just an example. The microphone to pick it up is a limitations, but the gain is:

- reduced power usage as the signal generators are not power-operated

- less waste as no empty batteries need to be discarded (if non-rechargeable batteries are used)

- improved security because the signal generators are not connected to the internet, reducing the attack surface.

If you are constantly looking at your smartphone and ignore the real world ... yes ;-)