I think that's a bit beside the point. We all use physical money. An executive that respected the vox populi would leave this for the legislature, where everybody has elected representatives that can debate, wheel-and-deal, and act on that voice of the people.

There's an awful lot you can do, but shouldn't.

The President is also an elected representative. This isn't beside the point: if it's not legislatively mandated, this is American democracy working as designed.

If the voice of the people is the concern, there should just be a referendum. I for one would vote to save the penny.

As I understand it congress mandates which coins _can_ be minted and their specifications (denomination/physical size/markings/etc) then leaves it up to the Secretary of the Treasury to determine how many need to be produced to meet demand.