Are you going to argue that “no-holds-barred” – as in, fighting dirty – isn’t negative?
No, I'm going to argue that "no-holds-barred" is not "political operative" and that adjectives modify nouns. If you see the phrase "evil dog", are you going to assume that must mean all dogs are evil?
I'd also argue that you're wrong about what "no-holds-barred" means too. After all, this is actually from an article championing the person in question. You misread a compliment for an insult because you're operating on the preconceived notion that both "no-holds-barred" and "political operative" are negative terms when neither are.
Are you going to argue that the system providing little control and no remedy isn’t a bad thing?
No, I'm going to argue that this question has nothing to do with showing that "political operative" is a pejorative term.
The other three examples are too out-of-context to know if they were complimentary or derogatory.
That didn't stop you from trying to argue about these two above, when you believed that arguing about them out of context was in your favour. The other examples are just more inconvenient to try to twist into somehow showing "political operative" is a pejorative. And, as we've seen, context is not friendly to your assumption.
The article is mostly paywalled, but here’s a salient sentence from the first paragraph where it admits I’m right:
How do you go from "it’s wishful thinking to believe the public imagines political operatives and staffers to be like The West Wing" to "political operative is an insulting way to refer to political staffers or politicians"? This isn't even getting into how the term is clearly and explicitly used in the headline in a way that indicates it as a neutral term that just describes a job, and that it will be used that way throughout the article.
The other two things you cited are from self-described “political operatives” themselves, and of course nobody believes themself to be the villain!
People aren't going to refer to their jobs in a pejorative way either. Did you forget that you were trying to say calling someone a "smart politician" is better than calling someone a "political operative"? You weren't saying all politicians are bad so nobody would ever admit they were one.
Again, where are you getting the idea that "political operator" is a term with a negative connotation?