Your thinking comes from a basic, although common, misunderstanding of money. Money cannot "accrue value" as it is nothing more than a unit of measure for real resources, not a commodity. The things money can buy may gain or lose value according to demand and their scarcity, but a dollar will always be worth one dollar.

Our currency-issuing government creates money to provision itself and pay for private sector programs it legislates. However, it is only the ability to tax and demand payment in its unit of measure that drives a demand for its currency. Because everyone needs that currency to pay taxes it is accepted as the denomination of trade and commerce, allowing the government to fund itself without need for revenue. The federal government never needs its own dollars back to enable its spending, but it does need us to need its currency.