Firstly I don't believe at all that only the 'rich' should have children. And yes, if you are working you shoudl be able to afford to support your family. However, I don't think that people should have 4 or 5 children because they want to but cannot afford them.
I know you are passionate about homeschooling Feeble but I think the issue is that when you start making exceptions the system becomes even more difficult to manage.
I am probably in a more unusual situation than many as I see both ends of the salary spectrum. I took a career break after my maternity leave so I have been a SAHM for 3 years and we live solely on DH salary, without any benefits. Almost all of our friends are earning beyond the £36k mentioned but many of them are choosing not to have more than 2 kids due to financial concerns. At the other end of the spectrum I work with many families on very low incomes and I see daily how they struggle. I just don't think that we should be having large families when we know in our heart of hearts that we cannot afford to support them.
I haven't suggested making any exceptions, just pointed out that situations arise often (not just to do with homeschooling, I also mentioned disabled or social uncomfortable children) which means it is better for one parent to remain at home.
I have also said that one person working long hours should be able to support the family, none of that suggests there should be an 'exception' for homeschoolers, there shouldn't have to be.
I agree with the points about large families but I do not think cutting tax credits to working families will affect that at all. If anything it will exacerbate the problem as people will continue having kids to continue to get income support/tax credits for their families.
Rather, it would be best to cap child benefit after say the third child, to put a loop hole in council tenancies that state if you have more children than your council house can hold, you will be expected to move into the private sector to find housing (so you will not be rehoused time and time again because your famiy size has increased) and insist on community involvement to receive benefits. I would also stipulate that if you wish to receive benefits, you have some form of proof regarding birth control, be it the 5 year injection, the implant or a coil.