(1) Having a house without a mortgage means that your economic conditions are relatively good, you can afford a house without a loan, and you have at least some economic strength.
(2) No mortgage reflects from one aspect that you live within your means and don't like overdraft consumption. Your consumption can be controlled within your income, which can give people a good impression of life.
(3) The blind date has a greater sense of security and will not worry about becoming a "house slave" immediately after marriage.