I smell an insurance company behind this
Like most restrictions airports now place on access, these local rules often come out of a 'what if' question asked by an insurer.'What if' there is an incident involving a companion animal? What steps have you taken to document and control the presence of animals airside?
With proprietal interest, which airport owners have, comes proprietal obligations to control, or at least have a means to monitor, what goes on on your facility.
Insurers need to be rounded up, placed in a pit, and ignited. They are destroying this country.