Nobody here has sufficient information to know what's fair.
It could be that they're a divorced couple where they shared care from the start, she got a fair settlement, and is now being greedy, as the assumption seems to be from most.
Or they could be an unmarried couple where her far lower earning capacity stems from her having been primary carer for the earlier years of their children's lives, before he left her for someone else, and she wasn't entitled to any share of any family assets because domestic contributions aren't deemed relevant, and house, savings and pension are all in his sole name.
In the first scenario, she's being unfair in seeking CM and this is a reasonable step to block it. In the second, she's been screwed over financially and this continues.
It's not as simple as people claim. In contested 50/50 care cases the decision is likely to rest on what is best for the children, and fair in all the circumstances. That would include who stands to lose most from the decision - as the leading case determined. Whether people here think that's fair or not, that's the law.
And while courts don't generally determine this - a Tribunal hears benefit appeals, and then an Upper Tribunal would provide binding precedents, if taken far enough - rarely, some cases can indeed reach the High Court via Judicial Review.
I can't say what would happen here; none of us can, because none of us are experts on this area, and even if we were, none of us have the actual facts. I do know that in the absence of facts, a bunch of women are eagerly reaching for the version of events that puts the woman in the worst light, and the man in the best. None of us know if that's fair or not, so I find the assumption an interesting one.