I wonder if Shaw ever looks back at her career and how different her life was from how she pictured it.
I think if Relevance hadn't happened Shaw would be perfectly fine doing her job and working for Hersh and Control (as evidenced by the AU episode). She didn't have a problem with their methods nor their management style until they made it into a problem.
I actually think she preferred Hersh's or Control's style over Harold's soft touch approach to action but one thing she does prefer with Harold is, that with Harold she's sure even if they disagree there won't be a bullet with her name on it.
In fact, in the long run, I think Shaw liked that they can disagree with each other, that they can talk and debate. As a daughter of an Academic, I think Shaw would have been exposed to long debates and arguments between professors and students.
This was why Greer can never win over Shaw, when he finally had an opportunity to present his case 'Your team isn't as good as you think they are' he failed spectacularly and even went off topic.
It's not that Shaw can't see the ugly math, she proved that she could by giving back Cole's research to Special Counsel she could, you need to give her a reason to justify her support of the ugly math.
And this is where Shaw's higher ups in the Activity failed her, Shaw will give everything on the line for her cause and for the people who are a stand in for the cause but she also requires that they be loyal to her too.
There is a reason why Future Starts Slow is Shaw's anthem:
And after all God can keep my soul
England have my bones
But don't ever give me up
I could never get back up when the future starts so slow
Loyalty is literally written in her skin: Semper Fidelis.
This is where Harold and John proved themselves time and again, and not just to Shaw but through their actions, the way the selflessly keep saving people.
It wasn't an easy road, Harold and Shaw clashed in early s3 (which btw I always thought they would but early s3 failed me in how they chose to portray it. Harold suddenly became a fussy aunt and you can see the writers had a hard time writing Shaw until Razgovor) because they were similar and Shaw was used to operating on her own without much oversight-- Harold has a tendency to micromanage.
One of the few things I wish season 5 had time for was Harold and Shaw's dynamic, I really believe by the time season 4 rolled around Harold and Shaw came to an understanding, they even had a mutual bond about John's increasingly reckless moves as Detective Riley. He trusted her to play Mission Control using his computer, we know he gets possessive about his computer.
And then in 6741 we know that in Shaw's psyche she was mad at Harold and she wanted Harold to apologize. I don't think this is something, even in Shaw's internal headspace, Shaw expects from Control.
Control would never apologize, even when she's clearly in the wrong, case in point: the ferry bombing.
She can lay everything on the line for the mission but she also needs to trust the people she's working with Harold might have a lot of faults but that's one thing Shaw can count on with Harold, there would never be a knife at her, to quote Angel of ATS, personal back.