Unless you want to improve the relationship between nobles and adventurers, and I am unsure that is something desirable...
That seems desirable to me. Not in the sense "nobles and advies should play nice together", of course, but in the sense that they do play the same game. I see this as a personalized addition to the bounty pot mechanics.
To address most of those problems I'd suggest limiting it to one house per knight with a minimum rent of 10 gold. I wouldn't put a restriction on how many houses an adventurer could lease, but rather make it hard to get them and unlikely they'll get their hands on all of them.
I would do the inverse and limit it to one house per adventurer. What commoner has two houses? This would also reinforces the social status aspect ("You live in my house at my sufferance, you better do what I tell you.")
