Custardo, I think you've lost the thread of your own arguments.
Your basic starting point was that you don't think PSHE, vaccinations, blah de blah should be done in schools because this is the parents' job.
You recognize that not all parents are able or willing to do these things or to look after their children and support their educataion in all sorts of ways.
Your answer to this is parenting classes.
You have said explicitly that the Government is not investing in parents or supporting them adequately with the assumption that if they did all of the problems of inadequate parents or all the failures of adequate parents would be resolved.
I have pointed out to you several times that the Govt DOES invest in parents and parenting. I have given you many, many examples of ways in which the government helps parents to parent from midwives, to Parentline to FE colleges etc and also nurseries.
If I was a struggling (financially and as a mother) parent there would be a great deal of support on offer to me.
If as a middle-class, educated, not rich but not poor parent wanted support it would be available to me. I wouldn't hesitate to phone Parentline if I thought it would help and without being at the point of desperation. I have used and benefited from Sure Start, my HEalth Visitor (who I called when I was struggling to get my dcs from tit to teat and who carried on visiting me after this until it began to drive me mad), all the info I was given when pregnant and after giving birth (which included copious amounts on healthy eating and on vaccinations).
Regardless of my financial situation if I was evidently struggling to parent there are a great many organisations who could and hopefully would (depending on the severity of the situation) intervene. Midwives, HEalth Visitors, teachers, social workers, GP blah di blah.
Yet in spite of all of the support above parents can and do fail. Even parents like me (who once again is putting off getting my dc her MMR booster).
Your solution to these failures once again is parenting classes yet you have not outlined the practicalities of this (how many? When? What do you do with the kids?).
I agree with you that people need to be taught the skills and information to be a good parent but I think the vast majority of this information and skills is helpful to all aspects of life. For example, learning how to eat healthily and feed a family, learning how to budget, learning how to respect others and communicate, the importance of exercise, learning how to manage difficult behaviour, learning about contraception. (What else did you envision the parenting classes would consist of?) I think the best, most practical time to teach this stuff is in school as part of the curriculum and as part of PSHE. I think a lot of it already is being taught and there needs to be more of it and better.
Custy, compulsory education is called SCHOOL. You cannot force adults to go to any sort of parenting or other classes (unless there are very special circumstnaces like in place of a fine or prison sentence). This would cause massive resentment. For a great many parents most of what would be taught in these classes would be irrelevant so it would be a massive waste of time and money for them when that money could be targeted at parents who really need the support (like through Sure Start).
But also you cannot define and break down all the zillions of bits of knowledge and skills that good mothers and fathers use into a few classes called 'parenting' classes.
If you've had a poor education yourself you're unlikely to make a good role model or help support your child's education without a hell of lot of motivation, hard work and support. If you've never learnt how to count or cook or read or exercise or respect others then you will struggle with many aspects of parenting.
So in a nutshell what I'm saying is the best way to invest and educate parents is through schools not just in the sense that our students will all too quickly become parents themselves but also by involving parents in what schools do. I think getting existing parents into school and more involved in their kids education could make a dramatic difference to the kids, their parents and their relationship.
As for vaccinations and eye checks I think we've gone about as far as we can with this. Most parents are thankful that these things happen in school. Having these things happen in school is certainyl more efficient and less disruptive for kids and it means more kids are likely to get these things who might otherwise not. It does not mean that parents are any more likely to abdicate their responsibility or rely on schools any more than they will stop feeding their kids tea because they have lunch at school. That argument is spurious and there's no evidence for it. Most parents do not see this stuff as threatneing or interfereing or taking over their role any more than they would see a teacher supervising play or reading a story in this way. If you personally don't like it then that really is your own and a minority opinion which has no basis in fact.