Larry, you're making a mistake in assuming that pre-school-age childcare = nurseries only. There are many forms of childcare other than nurseries - nannies, childminders, au pairs to name but three.
I don't understand your communist argument. Shall we scrap the NHS then as well? What makes one state-supported organisation ok and another not?
You can't separate income from gender very easily. Women are the poorer members of society and we still have a gender pay gap that is MOSTLY due to the fact that women have caring responsibilities. Therefore you can't say it's about income rather than gender because the two are inextricably linked.
Your argument that education is different because children need to go to school and therefore this has a benefit for society as a whole could be interpreted as saying that what women want and need doesn't matter because it doesn't benefit society. Clearly many women DO want and need better quality, affordable childcare. There is a lot of demand for it. Given that women make up 52% of the population, there is an obvious benefit to society. THe only way that doesn't work is if you consider society to be made up of men, rather than women.
BTW I'm not arguing that all women should put their children into childcare. As I said earlier, I think there is something wrong about a society that would force women to work and hand over care to a paid professional when that mother would rather care for her own child. What I'm arguing is that child care needs to have a clearly defined economic VALUE (which isn't the same as being physically paid for it). So that SAHMs can receive tax breaks and rights to pensions etc to the value of for example, and working mothers can actually afford to go to work. Most people have jobs rather than careers, which means that most women cannot afford to work without significant family involvement. 4 in 5 working mothers use family/friends rather than professional childcare. This is a vast industry in its own right, but because it is carried out by women, for women, it doesn't seem to count.
Everything I have said above would apply to male primary carers as well, so it would benefit everyone.