I have read the 15 vs 30 year term mortgage debate for decades. And listened to all the arguments against getting the 30 and investing the difference. I went with the 30. At the 15 year mark (2012) I owed $265K, but had nearly $359K invested. Not quite $100K delta and to many, not worth the risk. But, since then, the S&P, with dividends reinvested, is up close to 300%. Yes, I am glad I didn’t listen to the anti-debt crowd. (Keep in mind, also, that 15 year period ending in '12 contained 2 crashes and the worst decade in a century. Even then, the years since have more than made up for it.
Let’s look at the risk I took on. In the 100 15 yr periods from 1900-2015, the lowest 3 were below 4%. But barely. Had that been the case, I’d have been a bit behind in year 15, but the years since would have made up for it. And still produced a substantially positive result.
To answer your question - that one would take the money saved and not use it wisely. The anti-debt crowd makes one flawed assumption. That the average person isn’t responsible. The fact that some 50% of people carry a balance on their credit card leads them to give universal advice for everyone which is suitable just to those 50%.
If the interest rate were, say, north of 6%, the time for success becomes longer and the risk a bit higher. But with fixed mortgage rates so low, literally zero after taxes and inflation, methodically investing will give a positive result.
To be clear, if those anti-debt peeps sleep better at night for how they’ve arranged their affairs, then they are doing the right thing. When asked what ones stock/bond mix should be, I say stocks should not be so high a percent that you lose sleep. That means a different number for each of us.