The problem with that arrangement--- having an investment account make your mortgage payments--- is that it creates a reverse dollar-cost averaging situation. A 15 year mortgage at your interest rate, for instance, costs $7.84 a month per thousand to service or $$94.11 a year. If you have an equal amount invested that means you have to have a 9.41 percent return every year to avoid being forced to sell some shares to make payments. Have a few bad years and your investment fund will never recover.
I do believe some older people can reasonably have a mortgage. The operative word is "some"--- if you live in a state with income taxes and have relative high real estate taxes, if your income is well above average, and if you have a substantial pension that can be used to make the payments, then a home mortgage can be used to provide a modest amount of leverage for your total portfolio.
But for most people having a mortgage just creates problems and may actually increase their tax bill because providing the income to pay the mortgage may trigger the taxation of Social Security benefits.
Scott