Side note: I doubt this is actually "AI". Probably some heuristics.
Price-fixing is not a right in the US. It's explicitly illegal.
We as citizens should be strongly opposed to anything that makes housing more expensive because it contributes to homelessness, which is much more expensive than just forcing landlords to actually compete with each other (you know, like the free market is supposed to).
The biggest threat to a competitive market isn't the government in the US. It's the accumulation of power by a small number of actors who control the majority of the supply side.
This conflicts with our moral sense (in part because there's nowhere you can go to opt out) so we backstop it with entitlement programs. But the premise is a least in principle fairly sound; not as evil as what you articulated.