Would such a strategy legally work in the USA?

Here in the Netherlands, a plan to regulate maximum rents seems to be much more promising.

We will know if it worked in about 2-3 years.

TL;DR - This is a bandaid solution that won't have much impact short term or long term. We need millions more houses, unfortunately building houses is an expensive endeavor and no one is going to do it without a huge payout which only comes from building huge houses. Governments need to provide incentives for developers to build houses people can afford.

I'm against investment firms owning SFRs and renting them out, but this is a very small part of the problem. If we converted every rental house into an owner occupied house it wouldn't actually increase the number of houses available, it would just change some renters into owners. Then what?

The actual problem is that we don't have enough houses. We need millions more houses to meet current demand (for owners and renters, not everyone can or wants to own a home), and we're getting further behind each year.

We need to make it easier for builders to build homes, whether that's private development companies or publicly owned housing councils. We need developers to build medium and high density "missing middle" housing as well as smaller units that are affordable to low income people. As it is, private developers don't build these types of houses because they aren't as profitable per square foot as shitty McMansions. Since housing projects take an extremely long time to complete, no one wants to tie up their money without a high return on their investment that they get through McMansions.

The federal government needs to step up and apply some pressure to change zoning laws and encourage development of missing middle and smaller houses. Some ideas on how the federal government can do that:

1. Withhold infrastructure funding to cities with restrictive zoning
2. Give grants to developers to pay for permitting and planning costs provided the developers have a minimum percentage of missing middle and small units in their developments
3. The federal government agrees to buy all of the small units from the developer at above market rates and then resells them to first time buyers, provided the developers meet the same requirements as point 2.
4. Give money to local governments so they can start effective housing councils that will develop affordable housing themselves

If we somehow manage reach housing supply and demand equilibrium we can't stop development. We need to keep building so we don't have the same situation we had after 2008 and end right back here 15 years later because all the developers walked away.