My read is that the CIA wanted to use Watergate to wound Nixon, blackmail him and keep him under their thumb, but they were too good at their job and destroyed him instead.
More detail is supplied in this Wikipedia article on Richard Helms in the “Helms dismissed” section:
https://en.wikipedia.org/wiki/Richard_Helms
Excerpts relevant to this topic:
“(November 20, 1972) Helms was informed by Nixon that his services in the new administration would not be required”
However Helms was a career Federal employee and so could not be removed from the government. Watch what happens next:
“Helms also suggested that since he could retire when he turned 60, he might voluntarily do so at the end of March. So it was agreed, apparently. But instead the event came without warning as Helms was abruptly dismissed when James R. Schlesinger was named the new DCI on February 2, 1973.[311]
The timing caught me by surprise. I had barely enough time to get my things out of the office and to assemble as many colleagues of all ranks as possible for a farewell. ...
A few days later, I encountered Haldeman. “What happened to our understanding that my exit would be postponed for a few weeks?” I asked. “Oh, I guess we forgot,” he said with the faint trace of a smile.”
Remember what Chuckie said—the intelligence folks have so many ways to get back at you....
Sometimes in DC it can get personal...