I disagree with your contention that we can’t use a business model to consider the funding of the U.S. Government and the value of dollar. The U.S. must trade on the world market for resources and that market will determine the value of the dollar. To facilitate global transactions the Government keeps book on its spending and its revenue and balances the difference with borrowing. This legitimizes the dollar. So while the dollar is a fiat it is legitimate because its value is protected by the idea that we will defend its value and telegraph any dramatic changes in our stance regarding the dollars strength and security.
If we decided to stop offsetting most of our deficit spending with borrowing the value of the dollar for the purchase of resources, especially those imported, the value would decline. Foreign sources of resources might even demand to be paid in some other currency or even in Gold. I mean really who would accept a currency that the issuer has declared it is free to print in unlimited quantity at will.
Remember in addition to our budget deficit we have a trade deficit. More dollars flow out of the country than flow in, well sort of, a lot of those outflowing dollars don’t really leave the country they just become deposits in American banks in the name of foreigners.