How does the Treasury General Account stabilize the economy?

The FED controls inflation by removing liquidity from circulation and reducing pressures for banks to add liquidity into circulation.

Arrows marked "created" show when reserve currency is debited from the FED thus creating the currency and crediting it to accounts in the economy.

Arrows marked "destroyed" show when reserve currency is debited from accounts in the economy and credited to the FED.

The Treasury keeps a TGA  daily balance of $300 to $600 billion, which means that it constantly removes that much more than it spends.

The constant generation and removal of money keeps the money flowing.  When money circulates to someone who saves it, then its value is reduced by interest accumulations when it is loaned out. Eventually it stops circulating due to lack of borrowers. 

Before the FED, wealthy individuals opened banks to provide credit/loans to community members. When borrowers requested "cash" so that they could pay help, banks generated currency backed only by the bank and useful only in their community. When members saved their cash, they could not use it to move to a new community and buy assets because it was not trusted in other communities.