Institutional investors only own about 0.5% of homes. If they're forced to stop buying, nothing will really change in a noticeable way. At best, small landlords and investors will scoop attractive properties up for slightly less.
Where they buy those homes matters though. In areas with lots of jobs/growth (often the areas experiencing the most housing price pain), that number is likely much higher.
Which of those do you think is likely as a result of the proposed action, and why?