Some people use them for travel, but primarily they seem to be stationary. The weight should be a consideration, and I know from the Tumbleweed people that they will tell you how much trailer you'll need for each model of their homes, but I'm not sure about the others. When we looked at a couple of models they told us to be sure about the capacity of the trailer once we picked a model (we have not yet made that decision, but it's still on the books) so that we did not have issues after construction.
As far as construction goes, there is a lot more bracing and design for wind in the plans that we reviewed than it sounds like went into what you saw. I don't think that standard framing would handle the stress associated with moving something like that at more than a crawl, and even then I'd be skeptical of the tile and tub surviving intact. The shingles, once they have been in the sun for a short time, would be OK with high wind (ours in Florida stayed on through three cat-3 hurricanes, so highway speeds would be OK I think). That said, once they get some age on them it would be a different story. I've seen a cat-1 peel an old roof like a banana...
1975 Westfalia (VW)
2014 Rockwood A122