Child benefit / family allowance replaced tax allowances. In those days, mainly men were working and so would claim the tax allowance for his children. In some cases the children never benefited from this at all (dad went straight in the pub) so the idea was that mother would get the money directly and father lose his tax allowance.
Of course, to benefit from tax allowance you have to actually be working or getting some sort of tax deductible income. If you weren't employed, you got no allowance.
I don't know the answer. If they made it means tested the higher earners, who already contribute a lot of taxation, will lose out, but those who live off benefits and in a few cases seem to have children just to increase the income, will not lose out at all.