Your new ideas really give no improvement, it adds a bit of personality but it doesn't work in small sizes (especially that 2 logo)
I honestly think that your original ideas for 1, 2, 3 and 4 were better and that while you could say it's lazy, it's uninspired and "it takes 5 minutes in PowerPoint", unlike the current BBC branding it's actually consistent and it's simplistic.
Lambie-Nairn's original BBC branding was consistent and simplistic, but it was also lazy, uninspired and "it takes 5 minutes in PowerPoint", That's because it focused more on the surrounding elements of the brand.
CBBC, Cbeebies (I might go so far with BBC Three, as it's serving exclusively on a online space instead of television) in my opinion, should not be affected by an entire cross corporation rebrand that affects logos because their entire brand is about personality, that's also one of the reasons why the original CBBC branding got ditched.
Other than that, If you released this with other brand material, such as the trailer end caps and ident concepts then this would of probably fared better (assuming they were good)