"They don't seem to have done a successful job of infiltration, if something as big as 9/11 escaped their notice."
I do not believe it did escape their notice. For reference --- CIA "Deals"
Don't forget, the CIA was starting to look like imbeciles to many people for their (supposed) failure to know of Nuke Development in India and Pakistan. And the flow of secret info to China.
And their $35 Billion/yr. was likely in jepordy. Aren't they a bit more secure now? And probably richer, too.
You're talking about a really high-risk strategy. I don't think a Dubya administration would have cut their budget much, before 9/11, but, if what you are suggesting approaches the truth, then a mere fraction of the truth now would destroy the whole agency, and their whole budget.