Don't make the mistake of equating inequality with poverty. Specialization is certainly a great driver of efficiency and wealth creation. This trade-off can be fine (in a rising tide floats all boats sense) but we have to keep our eye on the levers.
If you then urbanize, your inequality increases rapidly. But since we already have an urban, industrialized society, increasing density is not going to move the needle on inequality. It's arguable it'd move backwards because more people can suddenly live in a desirable area.
Logically I agree that this is a "distribution" or "social" problem, not solely "the fault" of urbanization (that is, the "correct" social policies ought to be able to mitigate the natural downsides).
Unfortunately, however, we have thousands of years of data in which no society has managed to discover what these correct policies are (or at the very least, they've been unable to be deployed at scale). This observation gives me some pause and causes me to re-evaluate some of my prior assumptions.
A poor reason to oppose urbanization, perhaps. But not a poor reason to oppose kneejerk urbanization without critical thought (a prevailing trend as of late).
Whatever the case, this force is a powerful one and should not be casually dismissed, even by those who believe workable solutions are (finally) imminent.
With tiny houses, you're going to get the opposite effect of the price being lower because if of the "tiny" aspect.