While what I've read has not pertained to high density housing in cities, I've followed the subject of Blackrock and other investment behemoths buying up single family housing with the sole purpose of turning them into rentals and jacking up the rent. The use a formula for who they target which are young professionals with little kids looking for a good school district (that's a laugh) and a safe neighborhood. Once they get them in as renters, they raise the rent WAY up. Not because they aren't already making a profit but because they want more. Between the financial firms and Airbnb, the residential markets have shot sky high so there's nowhere else for the tenants to move if they want to keep their jobs. I read about a new suburban development in Texas where Blackrock or Vanguard went in and bought over half of the brand new homes. They use front companies, as well - those ones that send out the post cards saying they want to buy your house and will pay cash with no inspection. Their agents are at all of the auctions, as well, outbidding the small time house flippers, often paying ridiculous prices to gain control over a local market. I don't know if this is the case in big cities but I don't know why it wouldn't be. Of course, in the cities there's the additional advantage of nothing new being built to compete against. While rent prices certainly do go up (like everything else) because of inflation of the money supply, there is still the greed factor.
These big investors are playing Monopoly. I'm not sure but suppose the libertarian answer would so be "So what? They bought it, they own it and can do whatever they want and tough shit for those priced out". Is that right? What I'm saying is it WILL lead to demanding socialism/communism which will result in more high density building, outlawing single family zoning (a big thing with the Agenda 2030 plan) and stack 'n pack living in 15 minute cities without cars. Eat ze bugs and get in your pod, essentially. Where do libertarians come down on all of this? I suppose they oppose zoning, as well? Dunno. Are investment firms owning, in some cases, 40% of the local housing market considered "free market"?