If you had a large amount of cash from the sale of one house would you pay for the next house in cash? I think I would to reduce my need for income. I loose the potential investment gains from the money I lock up in the house, but there's no mortgage interest to pay and without a mortgage I'll need a lot less income and hence will have a lower tax bill.
The lump sum argument is a little different than whether you would use monthly income to accelerate a mortgage or invest it.
This has been our experience: In mid-2008 we sold a house for a large profit. We invested $400K of that profit in income producing investments (dividends, preferred stocks, bonds) that kick off 7-8%. We take $2600 out of that account each month and used it to pay a $400K mortgage at 4.65%, with enough left over to pay property taxes.
Even during the markets ups and downs, we've been fairly steady as she goes (some banks dropped dividends but there were also great bargains to be found so it worked out). Last year we refinanced into a 20-year mortgage at 3.875%. So now our payments are a little higher (@ 2400 instead of $2200), but the pot is growing a little. So long as the amount in the pot roughly equals the mortgage, we know we can pay it off at any time. Yes, there is risk involved, so you do have to be able for the ups and down. But so far we've weathered the downturn at the end of 2008/early 2009 and came out ok.
The choice we had in 2008 was to take 400K and sink it into bricks and mortar, and then it was gone. Yes, we would have no mortgage to pay if we bought the house outright - but we don't have a mortgage to pay now either, as the dividends pay it. We expect that at the end of 20 years, there should be something left in the pot, and if it's still kicking off $2K+ a month, that's income we could use when we are 70.
Another issue is that we are self-employed and use 33% of our house as office/studio space. So 33% of our mortgage interest reduces not only our 25% federal and 5% state tax, but also our 15% self-employment tax. So it's an even more valuable tax deduction for us.