but then they make suggestions such as paying extra each month on your mortgage.
How else does one pay off his mortgage early other than by paying extra each month?
The principal and interest are fixed, no matter how much money you throw at them.
The interest rate is fixed.
The total interest paid varies depending on how much extra you pay towards the principal.
You'll pay the same amount every month regardless.
That's factually incorrect.
just put the extra money into savings
At 1.2%, if you're smart enough to put it in an on-line savings account.
until you have enough to pay off the mortgage
Which costs you 3.5%.
This way, the money is locked up in your home.
Who says that all of your money must be locked up in your home? (I'm sure that there are financial advisors who recommend that you throw every single spare dime into extra mortgage payments, but they're rare.)
Am I missing something?
Yes: the mathematical sense to see that a 3.5% loan costs more than than 1.2% savings earns you