Who benefits when you pay down your mortgage? Your lender! The more equity you have in your home, the less risk the lender has. If the lender ever needs to forclose, the more equity the lender can control, the more likely they will be able to come out ahead on the loan.
If you put "extra" money in a savings account, and later needed the money to make your payment (and avoid forclosure), the money would be available.
Money in the bank earns interest too. When you prepay your mortgage, no income is produced from the "investment".
Put your money in the bank or other investment, not in your home.
MMM