I think that whilst the actual rule-breaking aspect would frustrate bosses, if she were a correspondent (or someone not involved in interviewing/holding to account the Govt and politicians) then it could probably be brushed under the carpet and forgotten about come January. The main problem Sky has is that her job is to criticize the Government and politicians on their decisions relating to lockdown - having broken the rules makes her less credible, and begs the question: "why should the Government counteract her critiquing when she's broken the rules herself?". Having criticized those who broke lockdown restrictions (e.g. Cummings) this isn't a good look at all. She's front-and-center in Sky's news operations.
But while I do agree with what your saying. Something wider is being lost here. A journalist is there to ask the questions on behalf of viewers. It’s not about a presenter or journalist personally getting an answer to a burning question they have. It’s about the questions the wider audience have. Lines have been a bit blurred recently with Kay Burley, Piers Morgan ‘grillings’ becoming tabloid headlines. But this hasn’t ever been about getting an answer for Kay or Piers, or them pushing any agenda, it’s the viewing public of Sky News or ITV getting the answers or lack of answers depending on your point of view. Can guarantee most of the journalists who ‘went after’ Dominic Cummings following his trip to County Durham did so not for a personal agenda but because it was the issue of the day that viewers were angered by.
So no government minister will turn around and say “well Kay you didn’t follow the rules” because that’s irrelevant to the point. The issues moved onto whatever the next discussion is. If anyone did say that to Kay, it would be a weak defence, because as the old saying goes, two wrongs don’t make a right. It’s almost like saying an overweight newsreader couldn’t question a minister on obesity policy.
Don’t get me wrong, I think viewers - me included - will laugh next time she has to talk about lockdown restrictions on air, let alone interview someone about it. But I just don’t think it’ll be a huge impact on her ability to challenge others. Viewers may be less forgiving to her, but others will probably have done worse breaches in lockdown!