Looking at my original post I just learned that I am an intern. All this time I thought I was a planning director. Oh well. Anyway, yes, motels affect the demand for services. We have a permanent population of 7,500, but on busy weekends, spring break, and summer we go up to about 25,000. We have to provide services for that many people. They all use water, generate sewage, and drive on our streets. Some drive drunk, just like they do at home. Some punch out their spouses, just like they do at home. Some leave their valuables in their cars and come back from a walk on the beach to find them gone. The upshot is we have to provide services for a population of 25,000 but pay for it with a population of 7,500. We have a room tax, which helps, but it doesn't go into the general fund, which is where police and other services are paid from.
The enhancement of return for existing motels is not the real reason for suggesting a cap on motel units. It's because we are facing a major budget crunch (we laid off police last year and may have to cut even further this year) and want to limit the demand for general fund services as much as we reasonably can.
As far as legality, I don't think it would be a problem. Public health, safety, and general welfare goes a long way. We have capped the number of motel units in one part of town (with exceptions for B&B's, vacation rental dwellings, and motels of 10 units or less). It seems to be leading to an interesting market for older motels and for approved but unbuilt units.