A question to those arguing against early mortgage payoff, do you refinance periodically to take advantage of additional home equity and use the cash to invest? It's basically the same idea.
The incredibly-low interest rates available on mortgage loans today is what's driving the arguments for investing in lieu of early mortgage payoff. If there were no costs associated with refinancing, I would be constantly refinancing for as long as rates remain this low. Since there are costs associated with refinancing, I would probably refinance every 5 or 10 years or so if rates remain this low (would just need to do the math to figure out how often it's worth doing in light of the refinancing costs, which I haven't done), but assuming that rates will remain this low for so long is a huge "if".
Between 2011 and 2012, the rates were dropping rapidly and I refinanced three times and brought my 30 year FRM rates down to 4.875 to 3.5. Every single time, it was essentially a no-closing cost. I usually wait for a drop of at least 0.25%, to make it worthwhile. My last refi was in Aug 2012, with rates being near 3.5% for 30 year FRM. Unfortunately, the rates have not gotten much lower since then.