Most tweeters come in around 1KHz to 5Khz so there's no question their contribution is audible to pretty much anyone no stone deaf.
Heat is the problem, like anything you run power through it's going to get warm, run too much through it will get too hot and fail.
Amplifiers tend to run up to at least 30Khz, usually much higher so if it's in the signal to the amp it will go to the tweeter.
Ultrasonic frequencies will heat up the tweeter even though they can't be heard, a good argument for not using 'hi rez' playback.
Current Lash Up:
TEAC VRDS 701T > Sony TAE1000ESD > Krell KSA50S > JM Labs Focal Electra 926.