I don’t think either the official or unofficial rationale for that Executive order applies to copper pennies though. Our currency isn’t backed by copper, and hoarding pennies has a negligible effect on the economy because they’re basically worthless garbage that everyone hates.
The US Mint stopped producing the half cent in 1857, when it was worth what a dime is worth today and when the penny was worth almost as much as a quarter is now. We could ditch the three smallest denominations of US currency without having much of an impact on how people spend money. (How often do we need to buy something worth less than a quarter?)