Property prices are a big concern nowadays indeed, especially in high-demand areas. Complete (rich) strangers can come and outbid you.

In the most capitalist places (rich areas without rent control), you can rent a place for years trying to save money to buy in the area and see the rent grow fast enough that you can't buy and even have to leave as a renter.

Capitalism seems to work well for transportable things though, including cars. A house isn't transportable and it also tends to be something quite unique, which makes it incompatible with production in series. Even if you are somehow authorized and able to buy a cheap home, you still have the issue of the terrain, which can be more expensive than the home.

That being said I'm sure that there are people living on cheap (per square meter) terrain and happy about it, but that requires the ability to make the best of it, work on it or find work close to it.

Trust me, losing freedom you most probably consider as basic as air we breathe since your birth will stop such petty worries.

And no system would give you property just because it would be nice, neither did communism (I know since I grew up in it and saw its destruction of everything good first hand - it had to be bought for non-trivial money with good old mortgages, and only regime-aligned people could).

Maybe what you're calling capitalism is just oligarchy, in which case the nuance really doesn't matter.

If communism you wouldn’t own anything?

Billions are already "priced out" of owning property, why do you think you joining them would have any broader impact?

EDIT: I don't know why I'm being downvoted. Billions of human beings have absolutely nothing to their names, and they have no power to change things. Because they own nothing. That's a basic fact of our globalized capitalist economy.