The main reasons we do it as paid benefits, rather than allowances like the French, are:
a) Old fashioned sexist stereotypes that if the earner (typically the bloke) benefits from the extra he'll spend it down the pub and not on the kids
b) It's cheaper. Under a French style system where a family of 4 get 3 allowances, a basic rate taxpaying single earner family would gain by about 2500, a higher rate taxpayer by about 5000. Compared to about 1750 in child benefit. And the higher rate threshold wouldn't kick in till about 132,000!
Personally I'd do the following:
a) Get rid of child benefit completely
b) Restructure the tax system to a French style system which taxes families, not individuals, so a family would get an allowance per person not per earner. Ending the hypocrisy of assessing people as individuals for tax but as couples/families for benefits. Or a US style system where couples can chose whether to be assessed as individuals or families.
c) Raise income tax rates to make b) revenue neutral, ie the tax take remains the same.
d) Increase means tested CTC to account for the loss of child benefit.
That would result in a much bigger saving than the current proposals, the vast majority of the child benefit budget would go rather than 15% or so. It would of course piss off childless people who would pay more tax - but there are no handouts, just a fair tax system which allows everyone to use their allowance!