Article 1, Section 8 of the constitution gives Congress the authority responsibility to coin money. And in the coinage act of 1792, 31 USC 5111(a)(1), congress directs that the treasury "shall mint and issue coins described in section 5112 of this title in amounts the Secretary decides are necessary to meet the needs of the United States", with the list in section 5112 explicitly listing the penny (31 USC 5112(a)(6)). It's clearly intended to instruct the treasury to mint pennies without congress needing to proscribe the varying amount every year. It also clearly demonstrates the intent that pennies "shall" be produced.

https://spectrumlocalnews.com/mo/st-louis/politics/2025/04/3... https://www.law.cornell.edu/uscode/text/31/5111 https://www.law.cornell.edu/uscode/text/31/5112

The fact that all of that gives leeway for "'none' is all that's necessary" is why I said the legal basis was "shaky" and not "baseless". I think getting rid of pennies is good, but this is something that Congress needs to do, rather than continually abdicating its responsibilities.