Here rent can exceed mortgage monthly price

No doubt. Mortgage costs are but a tiny fraction of the cost of owning a home. If rental costs are anywhere near the mortgage cost you have found yourself one hell of a steal!

but housing demand doesnt go down, there are more buyers than units

You really think that if I show up with a billion dollars, I wouldn't be able to find a home to buy? That's silly. Demand is perfectly satisfied by the supply.

Those who desire, but lack willingness, are not satisfied by the supply, but they don't matter. They're just metaphorical 13 year old boys with a Ferrari poster on the wall, wishing that they could afford to have one. That's not demand, literally. That's just dreaming.

Everything else you listed goes against supply and demand theory

Go on.