Paying down the debt will not erase the dollar as long as the govt keeps spending the dollars it gets back in taxes.

Does your bank allow you to "pay down" your mortgage when you make payments and then give the money back to you to spend or invest? The "debt" is the money supply for the private sector and what you are describing is a balanced budget, which allows for no growth in the economy or population, and no way to net save in the govt's unit of account.