The reason it would be abusing their monopoly is that Firefox and Edge private mode browsers would not get the same treatment. Google Analytics would still be active for them in private mode.
The only ways out for parties here are:
* Accept the way technology works, that browsers are separate from code that runs on websites, and acknowledge that users can be tracked regardless of what their browser chooses to do
* Mandate that Google devise a way to stop tracking for all browsers in private mode (not a technically possible solution; judicial overreach), or just for Google Chrome (possible; but amplifies their monopoly because it would be a privacy incentive for users to switch to Chrome, a Google product; is also judicial overreach)
* Mandate that browsers have a standard way to indicate to websites that they do not want to "be tracked" and websites must respect that (and I don't have to tell you that this one is judicial overreach :) )
So, that's why I say the only way forward that makes sense for this case is for the plaintiffs to drop it. There's no acceptable judicial recourse for them here. They can lobby the legislature if they want to make it mandatory that ad networks respect the abandoned Do-Not-Track header.
I don't have a legislative outcome in mind, but I would like to point out that "Do Not Track" program was an attempt to do exactly what your second paragraph suggests, it just had no teeth and was entirely voluntary. I really don't think it's too big of an ask to not track someone flagging they don't want to be tracked, and if it takes regulation to do that then so be it. Ad-tech needs a wake up call to start behaving more ethically.