I don't think the CIA would need to or even be able to blackmail a sitting president. They are too busy being his second most powerful tool. Like a really good hunting dog. It doesn't matter if it bites some peasants so long as he does a good job for its master.
CIA: If you don’t let us torture people just because then we’ll make a scandal of you.
President: Oh no. I guess I have to let you. I have no power whatsoever. Can’t get the FBI on it, because they’re blackmailing me too!
The US government and intelligence agencies is not like what you see in the movies.
Jeffrey Epstein. Do you think it was coincidence that he had power of attorney over Les Wexner, who was involved with the notorious Southern Air Transport? There are many other intelligence connections, for instance Maxwell and her father.
The CIA is really the worst institution in the US government.
Also, Southern Air Transport was a CIA front company.
I'm not sure how a scandal during one presidency is comparable in your example to scandals that happened before a presidency. Further, you might recall that there was a 'strategic strike' attack in Africa as well as a contentious immigration ban in the first weeks of the Trump presidency, which, if I am following your logic, would actually suggest an attempt to distract from unsavory past deeds.
(Perhaps there is another cynical explanation for the Africa thing but it is probably not to distract from an, as you say, decades-old scandal.)
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.
It has been about seventy years so far.