No, it has to do with intent. I just can't see the current Doctor Who being written as though children are supposed to be its main demographic. I mean, maybe it's because I live in America where the show isn't as easily accessible, but the only people I know that watch it are adults.
That just might be why. It's being SOLD in America as a Sci-Fi show. It's ALWAYS been a niche show for science fiction fans in the US.
But, in the UK, I imagine, it's ALWAYS been sold as a FAMILY SHOW.
Would I show it to a five year old? No. But, is it something I would watch with my 10 year old, hell yes.
But let me ask you, what about the show itself, why do you not think it's written for the whole family? Is it the plotting? The themes? Which themes aren't for children?