That's a bit shortsighted. There are many valuable types of "work" in society that are not rewarded monetarily. Take for example, child rearing, community building, or caring for elderly/disabled/homeless people.
Should "the system" really push capable people into valueless jobs at the cost of meaningful jobs that have no monetary value?
If there is a deliberate policy decision to penalize someone for working on the grounds that "hey you would do better as a stay-at-home mom", that would be one thing; it would at least have some consistent internal logic to it.
But I don't think the UK's or US's systems are like that; they just got hobbled together by being pushed in different directions by various groups with conflicting desiderata that combined to produce ridiculous incentives, and those incentives should be corrected.
Moreover, to the extent that valueless jobs and valuable non-monetary jobs exist and can be identified, the proper response is to explicitly target them (either with penalties or subsidies), not just allow anti-market-labor incentives to exist because "hey, not every job is worth doing, you know?"
Should "the system" really push capable people into valueless jobs at the cost of meaningful jobs that have no monetary value?