Because that would require all landlords in every place anyone would want to live to coordinate with each other, and to also coordinate with builders to not build more housing in places people want to live to not build new housing. $1,000 per month, at a 3% interest rate, would support around a $400,000 mortgage. That's getting into the territory where you can custom-build a house, and is several times the cost of a pre-fab house. Two people on $1,000 / month each could cover cost of living somewhere cheap, and if rents get high enough in places where jobs exist, some people will just entirely opt out of working and go buy a house where stuff is cheap, which reduces demand in impacted areas.

Prices will go up by some percentage of the basic income amount, but that percentage will be less than 100% of the difference. The landlord might raise rent from $1000 to $1600, but not to $3,000.