https://constitution.findlaw.com/article1/annotation37.html
> Article I, Section 8, Clause 5 is known as the coinage clause. It gives Congress the exclusive power to coin money. The Supreme Court has also interpreted clause 5 as giving Congress the sole authority to regulate every aspect of United States currency.
That supreme court interpretation is from 1820 so it's both "settled law" and "an outdated ruling", depending on who you ask.
https://uscode.house.gov/view.xhtml?path=/prelim@title31/sub...
This law does not mandate continuous minting. So I think you are wrong that the Secretary of Treasury does not have the ability to say how much of a coin is produced day to day.
Legal scholars, such as Laurence H. Tribe, have noted that U.S. law grants the Treasury Secretary the authority to determine the quantities of coinage necessary to meet the needs of the United States. Therefore, if the Secretary decides that the required amount for a particular coin is zero, they are within their legal rights to stop its production.