I think absolutely NO: I understand these problems, but no one should be forced when talking about private properties and the right of freely using them. Private property is one of the most important things in life, as it refers to something is mine: we should not violate this.
I agree if the Government decides to incentive people who may rent their living place (maybe a second house), with many benefits, but forcing absolutely no
In this country we have the 3rd amendment to protect us against such actions. Although the actual amendment specifies 'soldiers' I believe the protection would extend to an attempt by the government to forcibly house any stranger in our homes.
There is a section in the Bill of Rights that says the government cannot force you to house and quarter soldiers. The British sent soldiers to the colonies, and to save money, told households these men are going to live here and you're going to feed them or we just kick you out of the house. That was such an outrage it is part of the Constitution's first ten amendments. The federal government saying you have to let strangers live in your home a la housing shortage is the same thing - a clear violation of privacy rights and property rights.