People don't save money, they save value. I don't know anyone who would recommend saving up $250K to make a down payment entirely as cash, because of course you're losing money to inflation. Given the huge run-up in equities over the last 30 years chances are you'd only have had to save up a small fraction of that had you invested it. And the more fiscal stimulus that went out, the more stocks went up.
I never mentioned about saving up $250k to buy a house entirely in cash. I said working 30 years to acquire a $250k house. It's about protecting value of your hard work - your equity. And regardless, it was hyperbole to show why prices rise when money is freely given out.