A short term rental is residential use, just like a long term rental is residential use. In both cases the property is used by people to live and sleep in.
The question is does local government have the right to regulate the duration of a rental lease?
I would argue it doesn't, and it's a blatant violation of sacred property rights for a government to take that power.
The answer to problems of noise is to enforce noise ordinances. Guests will keep quiet if they are told that the town hands out $500 fines for violations of decibel levels after curfew.
There are simple market and incentive based solutions but so many Americans are so quick to jump on the "Ban! Regulate!" knee jerk train these days.