Your libertarian opinion conflicts with the successful arrest and conviction of drug manufacturers, dealers and users in my small town. The adulterers and fornicators won't be arrested or convicted. We run the plates looking for previous involvements before any further investigation. If the hotel management calls, we have sufficient cause to knock on the door. The drug parties tend to be loud with multiple unregistered guests in the room. The stench from the meth cookers is easily discernible outside the door. Instant probable cause.
I think you're missing the point. You said that a car with a local license plate parked at a motel "usually" indicates a drug party or drug lab. That may be true in some cases, but I bet that the number one reason for a local car at a local motel is fornication. In my opinion and experience, there is no way that a judge who has any respect for the constitution would issue a warrant to search a room merely because the room is registered to a person who drives a car with local plates. That's a different situation from what you described in you follow-up post, where you indicated that the vehicle is registered to known members of the drug community, combined with other objective observations such as sounds, smells, and foot traffic.
Thank you for your efforts.
Add the fact that a drug lab will ruin the walls and furniture in a room and will make the next renter ill, if they are allergic to the chemicals.
Not all sex is consenting, often the rapist of children will rent a room.