I paid my mortgage off 10 years ago... then refinanced and now have a 15 year mortgage, which I will pay the minimum to keep up.
Here's why:
1. reduced risk - when you have a mortgage, you spread the risk of devaluation of the asset to the financer (banks, lenders, etc) - say there is another recession or depression, if things get dire, and you need cash, or need to move, or get rid of the house, worst thing - do a short sale or foreclosure and walk away from the house. If you have 100% equity on the house, and you need cash, or need to move, and don't have other cash available, you're screwed. The bank gets to share the risk of the house devaluation while I pay them a historically low interest rate, on a non-calleable loan that is guaranteed at that rate forever. Sounds pretty damn good to me.
2. greater flexibility - I have a lot more flexibility when my house is financed at such a low rate. I can put the money to work for me, invest it, start a business, or keep a rainy day fund. Nothing says I can't pay off my mortgage at any time should I wish, but it'll be my choice and no one else's choice. If you choose to pay off your sweet low rate mortgage, you've made a 1 way decision that may be difficult to replicate in the future (especially if you're FIRE and have no income, or rates go up).
3. increased safety - when you have money in your pocket (figuratively speaking) that you got out of the house, should some emergency happen (major medical event, rare emergency, etc), you can use that money to take care of the emergency. If your money is locked up in your paid off house, you can't easily get the cash out of your house to pay some urgent cancer fighting treatments to save a love one's life, etc...
4. more tax efficiency - if you are a high income earner, it is better to have the mortgage because the amount of taxes being reduced is a higher amount than someone who is a low income earner. In addition, the mortgage makes your property tax, and other deductions much easier to be utilized. If you live in a high property tax state, if you don't have a mortgage, your property tax alone may not be higher than the standard deduction, so property taxes may not help you reduce your taxes. If you have the mortgage + property tax, you can deduct both items to reduce your income tax above and beyond the standard deduction, so a much more efficient use of the low rate mortgage to leverage your property tax as a deduction.
Basically, if you don't pay off the mortgage, and it's a super low rate loan, and you take the money to invest, or as a safety net - provided you don't have a lot of other spare cash lying around (don't waste it), you're probably better off than those who choose to pay off their mortgage.
I took 60% of my mortgage funds and invested it. I have 40% in short term laddered investments that I can pull in an emergency. I sleep a hell of a lot better knowing that I'm more diversified than having all of my money in the house I sleep in (aside from my investments / 401k's, etc).