That is not what profitable means. Returns on investment in housing consist of: 1. rental yields, and 2. capital gains (i.e. change in price).
You cannot say whether housing is profitable or not (or affordable, for that matter) only by considering number 2.
There’s plenty of beneficial flexibility afforded by renting, even if you can afford to do either one.
Plus, if housing doesn’t go up in value like an investment, why would you want to tie up a downpayment and tie yourself down, losing money all the while? You’d have more incentive to rent and invest your down payment money.
Whether renting or buying is more expensive depends on your market’s outlook for property prices. But in an environment where they don’t go up, I’d definitely expect renting to cost more.
I’m pro owner-occupied housing. I think it’s good for families and good for the community/society. But in the hypothetical where it grows more slowly than inflation, renting starts to look a lot better than it does currently.