Wtf are you talking about?
Nobody's talking about not paying their monthly payment. The whole question is: Assuming you had enough cash to pay off you mortgage outright, are the possible advantages to buying fixed income securities?
If you bought something marketable like a UST and rates drop it instantly becomes worth more.
Yes you still have a mortgage to pay, but you sell the security for a profit, pay off your mortgage early and come out ahead.
If you bought a stack of $10000 bonds with different maturities you could structure them to pay out essentially as needed to make your payments.
If interestrates go up, you can just hold them to their various maturities and pay your mortgage over time. You roughly break even vs paying it off immediately.
If interest rates go down, you come out ahead by selling all the securities at their new increased value. Then pay off the principal.