First, if you pay off your mortgage, if you are like most people, you have now eliminated your largest debt and largest cash flow killer.
Second, you save at least 3.5% interest by not having to pay that amount.
Third, you can then protect a financial base of protection by moving it into an irrevocable trust (optional). This would typically be protected in bankruptcy or from liability that you incur.
Fourth, your future investing can seek a higher risk/reward because you are not as dependent on either cash flow or maintenance of principal.
Fifth, you have a piece of mind that cannot be matched.

Basically, it is like this: By paying off your home, you create a "financial base" that you don't have to worry about protecting as much. You can focus your financial army (future cash flow) on more productive investments. Alternatively, if you try to do everything all at once, your tolerance for risk and reward may be lower, while your actual risk would still be higher.

I get that the numbers may be better based on the typical assumptions. However, part of what I am saying is that those assumptions are oftentimes wrong due to changed behavior caused by having a primary residence paid for or not.