I don't see the problem with one child having it and another not doing?
DS1 got both the baby payment and the age 7 payment, so £500.
DS2 just got the baby payment, so £250.
DD got the baby payment, but due to our financial circumstances (redundancy) we came into the bracket for a higher payment, so she got £500.
It's just the luck of the draw!
As for paying your taxes and so being "entitled" it is the CHILD who got the money, and is hardly their fault if their parents are "too lazy" to work is it?