The only thing he does not have unrestricted access to is Justice department stuff (e.g. FBI), although there'd better be a damn good reason to deny it to POTUS if he asks, and legislative branch secrets which really infrequently comes into play. That's due to the whole separation-of-powers, checks-and-balances thing. But security clearances for everything in the executive branch stem FROM the president. If he wants to reveal some state secret, he can just tweet it with no consequences, or blurt it out while on the phone with foreign states. As Trump did on multiple occasions.
That said, of course there is a significant deep state bureaucracy which attempts at times to keep certain things hidden, even from the current president. But if the president were to ask about it, they have to tell him.
I also never said he had access to everything. Nobody has access to everything. Not arguing for a shadow government--it's already a fact. It happened when classification rules went from "what would harm national security" to "what would cause problems if American citizens found out we were doing this."