There's some sense in that. The current Child Benefit, IIRC, replaced allowances for children in income tax.
It is a long way back in time now, but.... I think, in my lifetime, as a parent (ie 1971 onwards), there was what was then called "Family Allowance", which was paid for second and subsequent children. I cannot remember the rates (plus, the passage of time makes them meaningless now), but, the was a rate for the second child, then, a lower rate for for subsequent children. Alongside that, there was a tax allowance (on the husband's tax code) for child or children (also, I think, a "married mans allowance"). At that time a wife's tax affairs where lumped in with the husband's tax affairs, again, from memory.
At some point, modernity and fairness struck, and, wives were deemed actual people and capable of having their own tax code etc. Also, perhaps not at same time, tax allowance for children was abolished and "Family Allowance" was increased, and, extended to include the first child.
"Family Allowance" was made payable to the mother, rather than the father. Presumably, exceptions were made where the Father was the single parent. Bear in mind that for the most part, at this time, "benefits" were collected from the Post Office, using a "Benefit book" of tokens, rather than paid into a persons bank account.
In addition, the "Married Man's Allowance" was renamed "Higher Rate Allowance" or something similar, and was made transferable between spouses, and/or claimable by (one) single parent.
I don't remember when these various changes took place, or, which Government of which party introduced them, but, I am sure, anyone who is really interested can find the information on Google.