Almost no one, used to buy a house outright, for the last 100 years at least and longer, actually. The old N.E. custom, of putting a small ivory round, into the newel SP ? ) post of the main stairway, once the mortgage was paid off, took many years to accomplish.
We bought this house with cash, have a sizable savings account,have an investment portfolio and did so when we were NOT 50+. And yes, I know of others who fall into that category too.
The fact is, more people own their own home now, with a mortgage, or without one, than at any other time in this nation's history.