How long do you think the CIA would remain as a legitimate organization if something like that happened? All it would take is one public statement by a president that CIA had threatened them and the organization would come down like a house of cards. The entire leadership would be in handcuffs and trying to explain away treason to the FBI who would happily hand them over to military intelligence organizations to rendition their asses to their own prisons.

There are tons of competing military intelligence organizations that would be happy to take over from there. The CIA as we know it would cease to exist in a matter of days.

Given that most presidents have huge egos that is a huge gamble for the CIA. All it takes is one tape to get out and then you've just started a civil war.