If my goal is to pay off my mortgage as fast as possible, why would refinancing into a new 30-year term (instead of matching my remaining years) ever make sense?

A fresh 30-year term can be the faster payoff route, because it separates your required payment from your target payment. A 30-year loan sets a low mandatory payment, and nothing stops you from voluntarily paying it like a 15- or 20-year loan whenever cash flow allows. You choose the aggressive payoff month by month. A 15-year locks you into the higher payment whether or not the rest of your financial life cooperates. The risk of the shorter term is real. We watched a homeowner in Georgia refinance into a 15-year at a rock-bottom rate, then lose a job. The high payment became unsustainable, credit-card balances piled up, and they eventually had to refinance again, at a far higher rate, back into a 30-year, worse off than before they started. Had they kept a flexible 30-year and simply paid extra, the emergency would have been far easier to ride out. That is the advantage: a lower required payment is a buffer. If a job loss or emergency hits, you drop back to the minimum on your own terms, rather than asking a lender's permission to refinance or tap equity at the worst possible moment. One honest condition. The reset only works if you actually send the extra principal. Take the fresh 30-year, keep the low payment, and spend the difference, and you have quietly thrown away years of amortization progress. Choose the reset deliberately, with the discipline to pay it like the shorter loan, and you get the same payoff speed with an escape hatch the 15-year never gives you.