It is the multi-family rules that conflict with tiny villages in Austin, and many others. If you're seeking to build a multi-family "thing" on a plot of land, it has to be zoned for multi-family use, and the permitting process for that is much more complicated and subject to a lot more rules. So, yes, it is the parcel sizes and number of houses per parcel that triggers the problems.
You can put one tiny house on one regular plot of land in Austin, most likely, without too much trouble.
Density is the alleged goal for a lot of the rules that prevent tiny house communities from popping up. But, there's nothing stopping anyone from putting one huge house on a moderate sized lot anywhere in pretty much the whole city, including places that are extremely sought after.
The moment you want to build housing for several families (or individuals) on one plot of land, that's when they insist it be condos or apartments with high density. There is no middle ground where people can have their own house and garden...either you're in a McMansion or you're in an apartment/condo.
There is recently an ordinance to allow a secondary housing unit on a lot, but the language of it makes it very clear there has to be a full-size house on the property and the secondary unit is to be a "granny flat" or garage apartment or similar. I don't know if this rule has passed yet, but it's been discussed quite a bit. I'm too busy lately to get involved in the minutiae of that, especially since it still doesn't actually fix the problem I have with the rules here. So, it may be that you could build a tiny house village of two tiny houses. Maybe you can get two lots side-by-side and build a four house village. Still extremely limiting, and doesn't help to resolve the sprawl problems that Austin has.
A friend who researched it found that building an "RV park" would be the only way to do it given current code and political climate...which has a limit on the number of permanent structures that can be on the grounds. So the tiny houses would have to be on wheels. And, homeowners associations and such will fight hard against permitting any new RV park or mobile home park, so the likelihood of any such thing happening near downtown approaches zero. Also, being an RV park makes it commercial construction, comparable to a hotel, rather than residential (though there are rules allowing permanent residency at RV parks with different taxation that doesn't include various "tourist taxes").
Frankly, a lot of this stuff comes down to wealthy people just not wanting poor people living anywhere near them.