Pretty sure any decent model could easily solve that anyways.
True, but often these things also track the mouse movements or touch inputs and analyse those to see if they match natural human input or not. Of course advanced AI would be able to simulate proper inputs but most bots today would fail this check.
I do it if I’ll be away more than just couple of days. Some of my hardware is pretty old at this point and I’m just a little paranoid about the possible fire hazard. I’m sure it would be fine to leave everything running but no real harm in shutting it down either.