I fail to see how it is a violation of your rights to be granted special privileges and, in turn, to be expected to be able to prove that you are entitled to those privileges.  Disabled Parking Permits and Service Animals are both special privileges.  One is already required to have their driver's license and vehicle's license and registration with them at all times while driving.  (Driving is also a privilege, although no a special one.)  The Permit cover letter is just another piece of paper to take with you and keep in your car.  Not something I would call an inconvenience or rights violation.  It is just because of actual rights violations that you describe—abuse of Disabled Parking Permits, depriving people who have real need of such parking places—that the policy was implemented.