stop minting and stop accepting is commonly separated to allow adjustment. so likely a later president will just add the second phaseout step.
I get that the U.S. is a much lower trust culture, but is it really necessary? The rounding is only for cash transactions.
you may need to stipulate a grace period during which stores are still obligated to take pennies, to slowly shake them out of circulation without every American needing to visit a bank for cashing in. But its also possible that isn't needed either.
In the 2nd half of the phaseout you may need a proper marketing campaign to remind people to cashe in before expiration. (common when other countries update their physical currency). But that is probably the job of a different sitting president anyway so whatever.
Heck, is this actual something that congress have say over? It wouldn't surprise me if this was actually up to the federal reserve to decide, and they seem on board.