Ostensibly the CIA continues to exist through your elected congressional leadership as an agency created by the National Security Act of 1947. Voters don't have to vote consistently and can choose to have one branch of government ideologically at odds with the others. This would be the CIA working for the people but without it being aligned with the President.
If Congress decided to end the CIA then they could pass a law abolishing the agency or pass laws that refine the things they can or cannot do, but they're not inherently beholden to the President. The legislative branch being at odds with an executive branch representative isn't inherently problematic unless you think the President should be king.
>"The legislative branch being at odds with an executive branch representative isn't inherently problematic unless you think the President should be king."
There's another lens: You could think this, and have it rooted in the belief that separation of powers and the "checks and balances" against political institutions should have expanded beyond 'Executive' <-> 'Legislative' <-> 'Judiciary'.
There are more than three institutions and checks and balances between them. There's also: a) the States as a foil to the Federal government (and vice-versa), and b) the jury.
Jury is really the ontologically-vested check and balance that “The People” receive, the rest are implied through negative rights (right to guns BECAUSE congress can’t infringe, right to speech BECAUSE congress cant abridge)
Jury is a positive right within the right of due process - AND the right of citizens to participate in - and is therefore treated as a compelled responsibility on members of the populace, that exists to quell concentrated power from legal proceedings. In my opinion, we should have had more of those - and “The People” should have been an enumerated institution within the political structure that offers more comprehensive positive rights, negative rights, and compelled (and tensioned) checks and balances against the other institutions (executive, legislative, judiciary, “state”)
> This would be the CIA working for the people but without it being aligned with the President.
If the POTUS feels the CIA is not obeying legal orders then he can roll heads till they do.