I'm not against the idea per se, but "institutional investors are buying up homes" is an effect, not a cause. Boomers demanded that "house values are never allowed to go down, only up" and put all manner of construction-preventing policy in place to make sure this happened, so
of course institutional investors showed up. If there's an asset class which is only allowed to go up, why wouldn't they?
Banning institutional investment doesn't remove the "can only go up" laws and mindset, so I think (assuming this even happens, which it probably won't: TACO) the actual effect on prices will be minimal.