Given, as Andrew said, most of the CBBC channel's airtime is when its target audience are in school, and Cbeebies' must be targeting a relatively small number of households, is there a good argument for keeping them as different services today? Parents of young children are no less likely to have access to iPlayer than anyone else, and the child-friendly versions of iPlayer should prevent other obstacles too...
Merging the two channels (though maintaining the brand) would presumably save several million that could go towards, say, BBC One drama or other services, and in tandem with other savings/ reductions might make more sense than the current set up.
From the moment it was announced that the BBC would launch not one, but two children's channels it did seem like overkill to me. My ideal would be one channel arranged like this: 6-8.30am CBBC, 8.30am-3.30pm CBeebies, 3.30-7pm CBBC. Ever since CBBC ditched schools programmes, it has seemed for it odd to broadcast programmes to an audience not available to watch it.
But I don't think doing away with daytime CBBC would actually save much money at all. It only shows repeats during school hours, with all new programming appearing during the breakfast and afternoon slots. It's questionable why CBeebies needs to produce so much new material, though, when its audience effectively renews itself every few years, so maybe there's some potential savings to be made there.
However I think if the BBC were so much to lay a finger on either the CBBC or CBeebies channels, there would be an outcry that would dwarf that surrounding the BBC Three proposals.