Moreover, even if we didn't have a deficit, the increased tax revenue would go towards paying down the debt, which we simply rearrange where money is located in the economy.
If we didn't have a national debt, the government would then lend out its surplus. If it didn't lend out its surplus, it would then be acting as the monetary authority and affecting the money supply rather than the velocity of money. If the monetary authority (Federal Reserve) did not like this, it could overwhelm any monetary authority behavior on the part of a central government. If a monetary authority didn't counter this type of behavior, it would cause a decrease in inflation.
However, the decrease in inflation would come at the price of decreasing real GDP growth and increasing unemployment. If you are advocating for the government to decrease inflation in this way, you are advocating for the government to reduce economic growth and increase unemployment.