Perhaps somewhere hotel/motel business license regulations prohibit long term stay. I can think of one reason why. In many places, 30, 60, 90 or 180 days at the same address and you can register to vote with your new permanent address. A small town with a big interstate interchange might have as many motel rooms as permanent residents. Enough motel guests registered to vote might be enough to vote out the locals and let some outsiders "take over the town". Who knows when some cult leader decides he would like to own his own town to house his cult. I think they tried this in a small town out in Oregon a few years back.

I once stayed in the same room over 30 days. Once in a while when the bill got so big, or at the end of the month, I would have to sign the charge and start a new one, but that was due to the hotel accounting dept. needing to close out that months books, not due to any length of stay restrictions.