That's not to say that corporate entities wouldn't be able to adapt and fill the power vacuum, but they wouldn't resemble corporations as we know them today, and they likely wouldn't resemble some of the silly concoctions that you sometimes see in SF (_Venus Incorporated_, etc.)
If a national government decided to let an independent fiat currency be developed by an independent corporation, and all the other corporations, such as banks, agreed to use that fiat currency, that currency would have the same value: you need it to trade for your needs because you get paid in it.
It is not clear why trade could not continue in the absence of the federal government, as all the banks would probably be willing to lend to corporations with good credit, and they would probably continue storing their reserves in those banks.
In other words, I think you assume too many magical steps.
When I read "Market Forces" (scifi) I thought, very entertaining but completely unrealistic. In the absence of government, maybe not.