>House prices tend towards the level where a mortgage payment roughly equals a rent payment (since they’re substitutable).

No these two are not direct financial substitutions. You are ignoring a down payment (or mortgage insurance), property taxes, maintenance, and the general risk that comes with home ownership. Monthly mortgage payments should be a decent amount cheaper then rent payments on an equivalent property.

Definitely worth properly modelling out both buy and rent scenarios including all related costs, the substantial tax benefits of the mortgage interest deduction, remembering you are paying down principal in the mortgage payment, and the opportunity cost of the down payment. But when I've done this the cutover point is usually fairly close to where mortgage payment = rent.

The other thing that's notable when you model the scenarios is how much of a difference it makes how long you stay in a house given the absurdly high transaction costs of selling in a house in the US. 5% realtor fees! $50k on an SF condo, $75-100k on an SF house.

Renters are paying all the same things you are, and are usually paying through the rent much higher taxes and mortgage interest. The only difference is they don't have variability in expenses (AC goes out) -- but neither does a large landlord.

Maybe not the first few years. Rent payments inflate and mortgage payments don't.