Making regularly early payments on a mortgage without paying it off completely is always a bad idea, because if you lose your job you will still have a mortgage to pay, but no money. If you make minimum payments and save/invest everything else, you will still have a mortgage and also a bunch of money. We are assuming this is somebody in the US with a 30 year mortgage at an absurdly good rate, by the way.
The only debate is then if you should pay off your mortgage in the year you FIRE as a lump sum. In this case think of keeping the mortgage as a hedge against unexpected inflation, while paying it off is a hedge against unexpected deflation. Inflation is probably more likely. Thanks to government backing, keeping the mortgage is also the best choice for expected situations. On the flip side, if there is deflation and a corresponding market crash and you have no regular income, good luck refinancing to take advantage of the new amazing rates which might be necessary to keep your house. In this case the mortgage is a risk. In all, keeping the mortgage might be best 95%ish of the time.
You might also consider your asset allocation. Someone with a lot of stocks may not benefit much from inflation protection, and might want to pay off the mortgage at FIRE to protect against that small chance of deflation. On the other hand, someone with a lot of bonds may want to keep the mortgage as protection against inflation. That is why some people say a mortgage counts as a negative bond.
In the end I am with Mr. Money Mustache and say that simply asking the question is a win-win situation, but only if you are considering paying it in one lump, hopefully because you already have all the money you expect to ever need.