I agree that it's less risky to set aside cash to pay off your mortgage in a lump sum rather than dripping it in all along. If you have an emergency, that cash is more flexible than a HELOC. Also, if down the road your mortgage interest rate seems ridiculously low relative to the interest rates you can earn on cash you'll happily drag out the mortgage as long as you can. And cash can be readily used if you find an opportunity more promising to invest in than paying off the mortgage in the future. To be sure, at this moment in time, interest rates on no-risk savings are less than mortgage rates, but if you even invested just 20% of those savings in equities (or whatever else you research that is higher risk) you'd probably come off better than paying off a lower than 4% tax deductible interest rate and still keep liquidity.
This is what I do:
With my rate (recent no-cost re-fi to 3.875 for 20 yr fixed loan, about 275K left on a loan for a house appraised at about 450K) I'm reluctant to pre-pay my mortgage, but I have a conscious awareness of a "bucket" of investments I will use to either cash flow or pay off this mortgage in ER. While this bucket is currently invested in a balance of stocks/bonds, as I get closer to ER, I will likely shift enough into safe investments to cash flow the mortgage if the the interest rate I can receive on cash is higher than 4% or to pay off the mortgage if it is not. So far, I have consistently been able to make far above 4%, and I can comfortably pay my mortgage on my income if these investments were to tank. Plus, we plan to sell and move to a lower COL area in retirement.