I don't agree. I think it's far better to have a universal benefit that anyone and everyone can claim and then "reclaim" it in tax from those who don't need/deserve it.
I don't know what the situation is now but additionally, when I was a child, family allowance was paid to the mother when nearly all the breadwinners were men. Therefore it was a way to ensure that at least some money got to the mother.
If the qualifying criteria is "X exists" then it's harder to scam, easier to detect scams and cheaper to administer.
Finally, it avoids the crazy situations we hear about where it just isn't worth people going to work at all.
The government is now talking about forcing all 16-18 year olds to continue at school but IIUC pay them to do this. Why don't we just pay that money to everybody and remove the zero rated tax band (or adjust tax bands however seems appropriate).
IMO the reason governments like means tested benefits is that there are people who are entitled who either don't know they can claim or are too proud to claim.
Tim.