As someone else pointed out if you have a large mortgage and pay it off you can live on much less $ if something does happen.
so the money has to come from somewhere and go somewhere.
if you're assuming spend all you earn or pay down your mortgage of course that makes more sense.
But everyone has a limited amount they bring in whatever that number may be. after you've maxed all retirement accounts you have a sum left over. That sum is then spent on fixed expenses rent/mortgage, utilities, food, water money that has to go out. then you hopefully still have a sum leftover.
So now what do you do with that sum
Lets assume to identical twins make all the same choices up to this point and each have 10k annually left over
Twin 1. pays down house
Twin 2. invests
with 10k per year extra to the mortgage on a 200k house twin 1 pays his house off in 12 years.
Twin 2 invests. at 8% return his money is worth 205,000 at the end of 12 years and he has a mortgage of 145,000
so yeah he is 60k ahead thats the easy math.
So both Twins get laid off in the 12th year or later they are likely in the same boat with the caveat that twin 2 has extra capital if he needs it
But now lets explore the what if they get laid off in year 11 or earlier.
We'll just use the mid point year 6
say they both have 6 months in an E fund but neither can find a job til a year later. so they need to live and pay their mortgages for 6 more months.
Twin 2 is SOL
Twin 1 has earned -5% return on his 10k savings over the last 6 years (remember its been a bad market) - and only has 50k of his 60k invested left.
but thats enough for him to keep making payments for the next 6 months. but for anyone here 50k should easily float you for 6 months esp. if you're jobless.
SO
what did we learn? if you want to pay down your mortgage then you should probably at the very least invest it and pay it off in a lump sum you will have less risk.
Assumption 200k loan at 4% over 30 years.