Having watched some of the shows I still don't catch the full appeal. Perhaps so you can claim you don't live in a trailer? Modern campers are at times better finished and likely to pass more stringent inspections. Throw in that trend towards slide outs on campers/trailers and they have space on demand.
Custom workmanship might be the real key, still it is a trailer by any other name.
If you're a millennial, you'd typically buy a starter home. Student loan debt and wages (having been disconnected from productivity in the 70s) cause workers to have insufficient income to devote to a "traditional" housing expenses. Therefore, a tiny home with less financial exposure is more attractive. Even though they're not dirt cheap, they can be of high quality construction and cost about the same as a traditional deposit on a traditional home.
There was a gentleman who posted his entire progress and his financials for the Tiny House on HN a few weeks back, and parked his in rural Texas. There was another young man who placed his on some borrowed land near the University of Michigan, as what he paid to build his was substantially less than what his dorm would've cost.
Remember, tiny houses get you around zoning laws. They're not homes, they're RVs/trailers. You can get much more creative about where you place them compared to a house you'd have to build.
I'm interested in it because I'm in the middle of building a Tiny house my self.