Horse, if I were to leave my job and take out of work benefits, housing benefit et al, start claiming CTC and CB (we get a tiny portion of this now, it's barely worth it), I would move from being a net contributor (by a fairly long shot) to a net beneficiary in terms of benefit in v benefit out. If a large number of people did so, more people would be sharing a smaller pot which would be desperately unfair to those who don't have a choice.
At the moment, we get tax relief on childcare vouchers, which is great. I don't expect the state to pay for my childcare, though a system like Australia's where it is more tax deductible would make sense to me, particularly when in my area, a full time childcare place is around 15K a year.
And obviously I benefit from the universal public services we all enjoy, such as schools, nursery provision, roads and the police, and the knowledge that there is a true safety net for people who are struggling.
True net contribution, rather than simple in and out of bank accounts, is much harder to pin down.
I'm lucky. I make good money, DH makes ok money, we both have employers that support us in working somewhat flexibly. I know a lot of people don't have that. So yes, I think the responsible thing - to my family and to society - is to continue to work, save for my retirement, support my family (including supporting my husband's choice to work) and pay taxes that support others who aren't as lucky as me. I think that's a pretty good example to set my son, too.
You won't get much argument from me on disconnect between wages and prices, but that doesn't alter the fundamental point of people making the decision of what's best for their children in their own circumstances. And for many, that decision is not 'quit work, take out of work benefits to stay home with my child' because that would be irresponsible to just about everyone.
On topic: this idea is still thoroughly bonkers.