In the upside down Bizzaro financial world we live in, you are indeed correct.

If the loan you got for a house was actually someone else's money that needed to be returned to them, then paying off the house is important and good.

But, when money is created out of thin air, getting the most thin air money (by mortgaging) is the way to do things. As soon as you pay off the loan, the money disappears. Everyone, especially you, are poorer.

This is why so many house people buy a house, fix it up, and then remortgage it for the new higher value. It pays for itself. It shows up better on the books. And the cash is not stuck somewhere it can't be used.