> In other words, a mortgage is another way to save money for retirement.

Yes, but that's missing an important bit: It is saving for retirement using the money that otherwise would disappear into rent.

If you had the option to live for free somewhere vs. buy a house, it'd be clearly far better to live for free and invest all the money for retirement. But rarely anyone has that option. It is really between spending that money on rent (money is gone) or spending it on a mortgage (build equity).