re: When to pay off the mortgage

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Wouldn’t the same be true if you paid off early? You still have the hard asset

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Yes but paying it off early means you used more valuable dollars to acquire the same asset. Why wouldn't I want to maximize the value of my dollars? Paying 2020 mortgage with 2040 dollars means I created value because the 2040 dollars are worth significantly less than 2020 dollars at the loan origination. The PITI doesn't change because the loan is a fixed dollar amount (not fixed value).

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An inflation hedge is an investment that is considered to protect the decreased purchasing power of a currency that results from the loss of its value due to rising prices either macro-economically or due to inflation.

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A mortgage is an inflation hedge because it allows you to purchase something today with money that is devalued in the future. Your 2040 dollars being paid on a house bought in 2020 are receiving the value of 2020 dollars. The money you use in the future to pay towards your mortgage was protected from inflation. If you bought a house in cash and had no mortgage then you used 2020 dollars to buy a 2020 house. The same thought can be used for paying it off early or even just paying extra without paying it off.