Make 3 columns, "mortgage paid," "investment", "no-mortgage". Pretend the house is $100k. With the mortgage you get to keep that money and invest it, so first row in "investment:" should be $100k. Put $0 in the "no-mortgage" column, put $-421 * 12 in the "mortgage paid" column. I got that number from a mortgage calculator, assuming $100k loan and 3% interest over 30 years.
Then in row 2, "mortgage paid" cell should be previous cell - $421 * 12. You will keep paying this for 30 years.
"investment cell" should be previous cell * 1.05. We assume the investment return is 5% over long term.
The no-mortgage column stays 0. You spent the $100k to pay for the house, so it's gone right off the bat.
Repeat this for 30 rows (years). Then at the end look at the difference between investment vs. mortgage paid columns.
And then get back to me and tell me if you still think that is a "smaller total return" :-)
Go buy a house that will increase by >5%/year, but then don't pay it off any sooner than you have to.
Make the minimum payments, and invest in something that will return a stable 5%+ with your remaining income.
Just because the house itself increases in value, doesn't mean you should pay down the ~3% interest rate loan any faster than you have to.
And really, once you've built enough via this strategy, you should either invest in a more expensive house or buy a house to rent afterward.
This is all the consequence of inflation and easy money/loans, but the smart money move is to never pay off low interest rate loans. This is particularly true when inflation (acknowledged anyway) is 6%.
Using the 6% number, you're actually gaining (on average) 3% on a 3% loan just by using the cash.