This reductionism doesn't seem useful. The population of people who want to buy homes has not grown in any way that is proportional to the cost of a home.
And I don't just mean in this thread, I mean ever. It's always hand-wavey "it doesn't work like that" when the evidence suggests that it does.
Why is your solution "put 3 families in this single-family home" and not "build more single-family homes?" If the market isn't "interested" in "terminating" single-family homes what makes you think it would be a good thing to do so, other than the fact that it would hurt a cohort of people you seem to hate?
If you got rid of height caps, minimum lot sizes, and loosened zoning capitalist developers you hate so much would jump at the chance to build medium (and even high!) density housing. No need to have the government steal homes from people to do it.