He should indeed. But if we're talking about should, then the emoluments clause should have been enough for none of this to have ever happened. And the base level ethical requirements to be President should have been law. And the American people should have demanded their lawmakers and officials enforced the law and legislated for white collar crime penalties. There were a millions shoulds before we got to this hot mess.
But here we are with a logistical issue of protecting a person for life from others, while similtaneously protecting others from him. Modernity is wild.