Trailers generally require vehicle registration to be towed on the road, and tow vehicles are relatively expensive. Despite already being on wheels, individual residents would still be unable to move their shelter themselves in response to being told to move on. And any organization that helps out with tow vehicles creates a centralized target to attack.

The solution in the OP of building this as part of a dedicated tricycle is pretty damn slick. "Yes of course officer I am moving along, as fast as I can"