I think I understand what you mean, but I am unsure rents are competitive. There is finite space around good locations (where "good" can roughly be defined as close to hospitals, groceries, services, transportation, high-speed Internet, parks and jobs). Wherever I lived I encountered two ways of setting rents:

* "Real" market pricing (e.g., France, Germany), where rent prices can pretty much go as high as needed (subject to some regulatory constraints). My experience is that rents eventually converge to 1/3 of the average income of people that want to live there. If you cannot pay up, you need to head for "worse" locations.

* Controlled market pricing (e.g., Sweden), which essentially means that you need to wait forever to get to the "good" locations or hope that a new "good" location will be built. The former is inaccessible to most people, the latter usually starts rents at 1/3 of the average income of people that could move in.

All-in-all, I suspect that UBI would eventually lead to increased prices in "good" locations, so the net benefit is negligible. Maybe people living in "less good" locations could benefit from UBI, but I feel that would still not help with the "flattening of wealth" that UBI tries to achieve.