Think of it this way. If I have a 30 year mortgage at 3% (for sake of argument), I know I can make fairly stable mortgage payments for 30 years and pay it off. Or, I can pay extra each month, and (for sake of argument) I can pay it off in 15 years? I will pay the same principle but substantially less interest over the, now shorter, life of the loan. So, what happens to that extra money that I'm paying each month if I don't put it toward the mortgage? Well, if I spend it to live a higher lifestyle, putting it toward the mortgage would have been a good investment. But, what if I dollar cost averaged it into the broad market each month (S&P)? Over 30 years, a 6% return is fairly reliable.
So, what happens if I loose my job part way through. With the 30 year mortgage, I'm still obligated to make that minimum monthly mortgage payment regardless of how much I've been paying up to this point each month. With no income, if I can't make the payments, I may be forced to sell the house or be foreclosed upon. If instead, I had been putting that money into the market which is much more liquid and earning on it, I can now dollar cost average out of the market paying that mortgage each month until the money runs out. That gives me time to get another job and go back to making mortgage payments from my income stream.
So, in reality you do hit the nail on the head, but it is not financial. It is physiological. If your personality is such that you sleep better at night knowing your house is paid off, there is value for you in paying it off early. If you do the math, it all depends on what kind of mortgage rate you can get at the time, how favorably mortgages are treated from a tax perspective, and if you believe the long-term market averages are a reasonable predictor for the next 30 years.
Thanks,
Jack