Housing costs are driven by local supply issues vastly more than big national buyers. They're just swooping in because the massive undersupply has made them a good asset to own in the past 15 years.

Building more housing. Building a lot more housing would make a much larger difference.

In terms of specific government actions, that's upzoning all residential areas and approving plans by default with chance for challenges if they fit within established (reasonable) requirements.

Are the mutual funds immune from supply & demand economics or are they just taking advantage of a shortage that means real estate prices go inexorably up? Maybe we could just increase supply and then the mutual funds won't be so interested in buying up the supply. Although I don't know how that's bad to begin with -- it's not like everyone wants to own their own home.