Land and property isn't infinite, and a person can buy up land they have no intentions to personally use in order to drive up scarcity, the value of all properties they own would then rise, and so on. There should be no limits on the things people can buy, but there should be a tax on things that go unused by the people who own them.

Rentals grow in popularity not because people love the freedom of movement between cities and countries, most of the time it's just the only thing they could afford in that moment, and the constant drain on their income paying rent could have instead been saved up to buy a home outright. Why not just have a system where you pay the local rent equivalent over a number of years, and then at the end you own the home? Assuming rent in New York is $1k, and buying a New York home can cost $900k, it would take 75 years of "rent" payments before you could own the place. Still, assuming you could pass it on to your kids, and you don't leave the city in your lifetime, it could be better than the current system, where you pay for 75 years and have zilch to show for it.

When the pandemic happened and people were leaving New York, businesses closed up and people documented all the shuttered shops by walking down the street with their phone cameras and looking in windows. The rent prices and things stayed the same despite the exodus, except not really. Bunch of people were given under-the-table deals where they pay less for rent for the year or whatever, but weren't supposed to tell anyone. Which makes more sense than keeping the prices sky high and people just accepting it despite all the local public services shutting down.

So the problem is that businesses don't want to present the appearance that they have lost value, even when they have. Land and property is bought up to prevent others making use of it unless they pay a high price. Sure, these things were never infinite, but rentals should only exist to serve a purpose, being a temporary place to stay for people who aren't sure where their job will take then next. If there's ever a time where rentals are the only option, where debt and mortgages are the only option, if people own places they have never seen and take steps to stop the people there from living there, then things are fundamentally broken.