There are some asset protection and lawsuit-avoidance advantages to having a mortgage. If someone is looking to sue you for something related to your online business, they are much more likely to come after unencumbered real estate vs if you have a mortgage on the property (even if its a small one, all they see is the secured interest, not the amount). A simple property search will tell the bad guys all they need to know, and if you own your nice home outright, that can be the equivalent of painting a giant "look, I have monies for the taking" bullseye on your chest.
Also, with fixed mortgage rates down around 3-4%, and the mortage interest deduction US residents get, you can be paying an effective rate of around 2.5%. That's pretty cheap money. If you are halfway decent at investing, even if you have the cash in the bank to pay the mortgage off in full, its a better use of those funds to invest anywhere you could beat that ~2.5% return.