Not in a free market. If demand is high, and supply doesn't raise to meet it, then prices will increase unless artificially suppressed.
Rent control could do that for rent, but has its own problems. As for owners, how do you tell someone they aren't allowed to sell their house for what someone else is willing to pay them?
If you do neither, are you implying that the third option would just be to tell would-be tennants to go look elsewhere because your neighborhood is full and you're not going to price out the people currently living there?
Sounds like it would work, until you realize most of the buildings are owned by landlords who want to cash in and get as much money as they can with the property they've invested in. They don't particularly care who is living in the property, just that somebody is there and that they're getting paid.
