Everybody should know that paying down a mortgage is equivalent to making an investment at the mortgage's interest rate - assuming either (a) the mortgage interest is deductible and the investment would be in a taxable account, or (b) the mortgage interest will not be deducted and the investment will be in an IRA. If you have a 5% mortgage and you are considering a 5% treasury bond, it's the same thing. I'd probably go with the treasury to enhance my liquidity and hedge inflation with my mortgage.

Most of us have higher ROI (and higher risk) investment options than paying off our mortgages. My mortgage is 3.625%, and I could grab some bonds, preferred shares, REITs, or MLPs yielding about 6%. This is the arbitrage a lot of people advocate, and that I am in fact practicing. However, the portfolio I would use has some significant risk. To pay off the mortgage is riskless. A similar risk free investment would be the 30 year treasury bond yielding 3% right now! I'll take my chances over the long term.

In terms of which strategy gets you to 25x expenses faster, mortgage payoff is it. A $100k mortgage at 4% interest requires a $477 monthly payment, or $5724 per year. If we multiply that expense by 25, we get $143,100 in invested savings required to support the $100,000 mortgage. Of course, you could save up $100k and pay off the mortgage faster than you can save up $143,100, so mortgage payoff gets you to having a NW of 25x expenses faster. This effect increases with the interest rate. At 6%, you'd need $180k in savings to cover the payments on that $100k loan!

The catch is the 4% rule describes an amount projected to last for life, whereas a mortgage is only 30 years. To be perfectly apples-to-apples, you'd need a complicated model/plan like a 5% rule for 30 years dropping to a 3% rule thereafter. But note how that plan magnifies sequence of returns risk. It gets complicated quickly.

So this comes down to a choice between (a) the higher ROI option, which is mortgage + investments, or (b) hitting 25x as soon as possible. Option A will make you wealthier long-term, but option B gets you over the 25x hurdle faster. The person pursuing option B can FIRE at a lower net worth than the person pursuing A, but at the same time the person pursuing option A probably has a higher net worth that is growing slightly faster and is much better hedged against inflation.

This is a case where optimizing will increase your time to FIRE.