I have a friend who has made a very nice mobile Tiny House.

The reports I've read on the prices of these make them pretty dear. In many places for zoning reasons they have to still be nominally mobile.

I don't understand what the big draw is over a towed RV

There are some: A tiny house in principle can be both wider and taller than an RV This may make them more efficient to heat, and make better use of space. RVs often are designed for more occasional occupancy even in use. E.g. they sleep 6, but don't have a good place to put the lawn mower.

The width of single wide mobile homes OTOH can be 13 to 16 feet (depending on highway regulations) 

So what's the attraction of a purpose built Tiny House?