I ran the numbers at $100,000, 30 years and a generously low interest rate of 5% on a readily available calculator.
The total amount is $446,774.43 after 30 years. I don't see anything "tired" or "nonsensical" about the facts.
Now, run the numbers on that same 100,000, 30 years, and a conservatively low market return of 8% on a similar calculator.
Look at the total after 30 years of compounding returns. (It’s a hair over $1,000,000).
Subtract 446,774 from that total.
See how big the delta is?
You are ahead by over half a million by investing vs. paying off the loan.
And that’s at 8%.
At 10% return (the historic average for the S&P), and the total is about $1.7 million, and you’re ahead by well over a million.
What’s nonsensical is failure to see the benefit of the arbitrage, of analyzing the best place to put your money.
An example - my own - starting 17 years ago, we got married and started investing modestly.
Now, we could have done what you suggest, and applied that investment portion of our cash flow into pre-paying the mortgage. We would have it paid off about now.
But we chose to invest. The result?
Our portfolio has a value that is more than ten times our current (3.25% refinanced) mortgage. About five times the total value of our house.
In your method, we would have a paid off house. No portfolio.
We are much father ahead because we invested. We could now pay off the mortgage and still have a substantial portfolio. We have about ten times the money that paying off the mortgage would have yielded.
It’s not even close