It kinda does, relatively speaking, in the long run. If you bought a house for 1 million at lower rates and the price goes up, you pay more than the next person who buys an equivalent house for 950k, at the higher rate. It’s still costly, but you pay less. When rates eventually come down again, which is likely, the person who paid less will still be better off then.
Rates are high and rising (compared to recent history), and prices are high and dropping. I’d prefer to pay the lower house price, than the higher. The rates end up the same for everyone over time.
Rents go up over time. Mortgages stay the same. So many renters end up paying more over time. The problem is the initial cost, both the deposit and the higher payment, compared to rent, for the first 10 years.