With the caveat that I'm new to mustachianism and investing and the like, this is what went into my thinking about prioritising paying off our mortgage fast (we still contribute the maximum to our superannuation accounts though):
1) We're in Australia, not the US.
2) We have a redraw mortgage with a reasonable (although not great) interest rate for Australia of just over 5%. No restrictions on number of transactions or size of transactions in or out of the redraw account. So paying off the mortgage fast does not lock our savings away - they're very liquid and takes at most 3 days to get money from our redraw account.
3) When the mortgage balance gets close to zero, I will keep it at very close to zero (so we pay very little interest) while I gradually siphon off the redraw account for an emergency fund, and then start investing in an index fund. And THEN I will close off the mortgage.
4) Interest from investments will be taxed at a high rate as DH and I are both in fairly high tax brackets at the moment. TBH, I haven't checked this out in detail but in the past I have earned enough interest from parking house deposit money in an online bank account to have to pay significant tax on the interest (and then talk ATO out of billing me quarterly for interest, but that's another story).
5) Primary residence does not earn any tax deductions in Australia.
6) I thought through 3 scenarios when I got the mortgage: pay off as fast as possible, pay off a bit extra (I have a 30 year mortgage) so it gets paid off after 15 years or pay no extra and do the full 30 years while investing. The first and third options make sense to me but the second seems to be the worst of both worlds. The first option gives me essentially 5.1% return tax free, minimises the total amount of interest paid by a lot, and most importantly (given I have several conditions that could kill or disable me anytime from 5 years from now or I could have decades - who knows, plus my job security is a lot lower these days than it used to be), peace of mind for owning a house that cannot be taken away from me. The third option takes advantage of inflation, which is relatively low at the moment, but risks 7) below, health issues, loss of job only partway through the 30 years etc and doesn't give me peace of mind.
7) Our mortgage rate is variable. In the 80's in Australia, interest rates went up to the high teens. There is always that possibility again in the future. Paying down fast while interest rates are at historically lows is good for my peace of mind. I do not want to be in worst case scenario.
8) Emotional reasons. I'm aware that this is not fully rational looking at it objectively but it is rational for my mental health and peace of mind. Having my own place is something I value extremely highly and I do not want to risk losing it. Paying off my mortgage fast is the best way to guarantee to keep my house, balancing the broader economy and my own personal situation.