Yes, it's pretty common to see a reduced monthly rate, though often the rate is without electricity.
We do it that way, too, though we also limit the stay to around four months at most, and we require pre-approval.
You'd be amazed at the number of building contractors who want to bring in an old, beat-up rig (usually with no water system and no propane system at all) and then run crew after crew through it. It's inevitably trashy, lots of trucks, lots of people at "drinking age," and lots of headache. That's what we found here when we bought the park, so we chased all of them off and now are pretty picky about who can come in on a monthy basis.