Is it troublesome to prove that the police station is open to stay in a hotel?

No trouble. You only need to bring your ID card to the police station under the jurisdiction of the hotel, verbally apply for "ID card certificate", and inform the police of your identity number or name, date of birth, place of residence and other information. The police will query the population information database of the public security network and contact the applicant. If it matches, a certificate can be issued on the spot.