I too, have always followed the same line of reasoning that you've brought up, until the Katrina/Rita scenario.
I don't know if people from those disasters are still staying in motels (I doubt it) but there were people/families being housed in local motels for at least a year. The same is true of motels and apartments in Houston and other large cities across the country.
I wonder how much damage FEMA ended up paying for (holes in doors and walls) in FEMA contracted motel rooms. I remember hearing one story of a motel owner who wanted these "FEMA tenants" to be moved out by FEMA because of the damages that they were doing to the rooms. FEMA refused (so the story goes), so the owner closed his motel, forcing the "FEMA tenants" to leave.
How much ($$$$$) did the Federal Gov't pay out in damages to thoses who sued over the "excess formaldehyde" fumes in the campers/mobile homes that refugees were housed in?
I'm saying that it may actually be worth the expense of having 1 or 2 such facilities for every 3 or 4 state area.
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QMC, USCG (Ret)
The best luck is what you make yourself!