Indeed, the concept of immunity is recognized in the American constitution for legislators in a limited way, so this isn't an oversight by the framers corrected by Robert's conservative majority, rather the lack of immunity for the executive is a feature and not a bug of our constitution, and all republican forms of government.
Ironically the American president now has more power than the King of England, George the III, at the time of the American independence. King George had to follow the laws of Parliament, as did all Kings of England since the passage of Magna Carta some 500+ years prior.
As of today our President no longer has to obey the Constitution or the law so long as the act is deemed "official" by the conservative majority.