I don't understand this. How does it reduce stress? Paid off houses aren't liquid and you can't really leverage them (in an easy way).

Option 1: a) Have home paid off with b) less liquid funds you can use in an emergency.

Options 2: a) Have low interest loan. b) Have money to cover low interest loan in liquid account. c) have much more liquid funds that can be used in an emergency. d) have more gains over 30 years

Option 2 is way less stress, even in the even you lose your main source of income.

I posted in another comment, but banks and lenders will do everything in their power to not foreclose on you. It's way more painful for them then it is for you.

Lastly, if you are worried about not having money to pay mortgage, then you don't have money to pay off property taxes or insurance, both of which are also risks to losing your home. Both of which are more risky than delaying mortgage payments. But with option 2, you have a liquid buffer to cover these, but not with option a.