I'm struggling with this same question. My first goal isn't financial independence though, it's being able to switch to part time work ASAP so I can be home after school for my daughter when she is school age. She is 2 now and in full-time care. The way I can see to do this is to get rid of the mortgage payments to decrease my monthly expenses. I'm not very concerned about what I could get with the long term gains from investing, because what it can't get me, as far as I can see, is time with my child. Paying off my mortgage quickly CAN do that.
That's fine, but mathematically it's worse than investing, then selling the investment to pay off the mortgage. You get rid of the mortgage SOONER doing that than paying down the mortgage (again, assuming you earn above your mortgage interest rate), and decrease your monthly expenses sooner.
Paying down the mortgage doesn't decrease your expenses until it's paid off, unless you refi to a smaller payment amount. So invest, then pay it off at once.
Investing and then paying off the mortgage will actually get you the time with your daughter sooner than paying off the mortgage accelerated along the way.
And I also don't want to rely on the market, especially for that. I'd rather take the safe route to my goal.
That's the one correct statement there that I will agree with. If that's the route you want to go, definitely do so. But understand that at that point it's an emotional decision, rather than a mathematical one.
People are trying to "justify" the decision. It's not necessary. If you want to do it, go for it.
But don't try to convince yourself that it is better mathematically, because it isn't. Just accept that you're doing it a slower way and giving up returns for security, and that's okay. Just like the debt snowball (which I'd never do) is good for some people - for psychological reasons, not mathematical ones.