The question becomes what if the President then uses their power to jail/execute political rivals? How would you rule that as unofficial? Tons of dictators jail rivals on the “official” business of maintaining order or peace or some other nebulous term. The presidents role to enforce law is so broad that it can be used to justify almost any act.
This, so much this. Nobody ever jails political opponents, obstructs justice and bullies media in their unofficial capacity. If there is immunity, it will be used to do all kinds of shticks.
