The principal and interest are fixed, no matter how much money you throw at them.
This is not correct.
If I pay an extra $1000 in principal this month, then my mortgage balance is decreased. So slightly less interest accrues before my next payment. That means my next payment will be slightly more toward principal and slightly less toward interest than it would have been if I hadn't made an extra principal payment.
This means that my principal will eventually drop to zero earlier than it would have if I had not made the extra payment, and I will end up making fewer total payments than I would have without the extra principal payments. Of course, the effect is even stronger if I make regular extra payments rather than a single one.
Like paying off any debt, you can consider this payment essentially a risk free investment paying whatever is the interest rate on that debt. You know that by making this payment, you reduce your interest payments over the coming years by the interest rate on that amount.
In comments you said,
you will pay your mortgage off earlier but you won't drop the amount required to pay each month. Look at a mortgage amortization table to see this.
This isn't because of the amortization table, it's because of the contract terms between you and the lender.
After you make an extra principal payment, a new amortization schedule has to be calculated one way or another. It would be possible to re-calculate a new reduced monthly payment keeping the number of payments remaining fixed. Or you can calculate a new repayment schedule keeping the total monthly payment fixed and reducing the number of payments.
It happens the banks prefer to do the 2nd of these rather than the first, so that's the terms they offer when lending. Perhaps someone more knowledgeable can comment on why they prefer that.
In any case, by reducing your principal you improve your personal balance sheet and build equity in the mortgaged property so that, for example, if you sell you'll keep more of the proceeds and use less to pay off your loan.