> Can you explain how someone is to hold the President accountable for an illegal act if it is committed in such a way where no citizen has standing to bring suit.

Impeachment. Criminal prosecution by a subsequent administration. Civil prosecution by public authority if the particular illegal act is one for which their is a public cause of action. Failing all that, retaliation by a subsequent, similarly difficult-to-punish President. (The last of which, obviously, is obviously fraught, but it's there...)