The fed don't need to take up any "leeway" they gave, advertising on money is illegal. OP is 100 years too late to the idea of putting advertisements on US money. Somebody already annoyed them enough they made a law against it before we were born.

US Statute 18 USC Sec. 475 (house.gov)

-HEAD-
Sec. 475. Imitating obligations or securities; advertisements

-STATUTE-
Whoever designs, engraves, prints, makes, or executes, or utters,
issues, distributes, circulates, or uses any business or
professional card, notice, placard, circular, handbill, or
advertisement in the likeness or similitude of any obligation or
security of the United States issued under or authorized by any Act
of Congress or writes, prints, or otherwise impresses upon or
attaches to any such instrument, obligation, or security, or any
coin of the United States, any business or professional card,
notice, or advertisement, or any notice or advertisement whatever,
shall be fined under this title. Nothing in this section applies to
evidence of postage payment approved by the United States Postal
Service.

I'll leave it to you to find the updated penalty in H.R. 3355 (pdf), passed into law as Pub. L. 103-322 in 1994 (protip, search for 475). Enlightening reading of how a bill is written to be unreadable by adding new phrases to hundreds of other statutes instead of being new law itself, with a senator-friendly name "Violent Crime Control and Law Enforcement Act of 1994" (unfortunately 1994 is too early to discover from the PDF properties that it was likely directly written by and lobbied for by an outsourced prison labor company like Federal Prison Industries to boost their labor force).

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Completely off-topic, but FPI's front company Unicor made me think of another orwellian labor company that changed it's name to avoid it's reputation.