BUT, if you can pay cash instantly for a house, you may save more than the renting costs, if the seller is willing to lower the price for an immediate sale, and depending on how cheap a rented place you can find and tolerate for a limited period.

Meanwhile, from the point of view of downsizing, there is more risk of a reduction of house prices, which will mean you get less for the one you live in if you have to wait longer, than there is of a surge in prices between selling and buying anew.

That is an educated guess, not a prediction!