Re; Doctor Who as children's programme, I think we all know that although Sydney Newman originally conceived it as an educational adventure serial for older children, those who would develop, and ultimately produce, the series had other ideas. This is indicated in numerous quotes from the likes of Verity Lambert and Philip Hinchcliffe, who, evidently, never approached making the series as if it were a childrens programme.
I think to look upon Doctor Who as simply a kids show is to take a terribly reductive and innaccurate view of it. The higher-ups at the BBC who didn't understand science fiction may have seen it thus, but the people charged with making it evidently did not.
Ultimately, I think that Doctor Who was only ever really good because, in the main, the BBC didn't understand or pay much attention to it and just let the assorted creative weirdoes in the DW production office get on with it as they saw fit. In many ways this gave Doctor Who the feel of an independent production and I think it is telling that the only times that the show saw a significant decline in quality is when edicts from on high were passed down to alter the content; "More humour, less horror" etc.
I think the disconnect between the corporation's idea of what Doctor Who was and how the writers and producers of the programme perceived it had a great deal to do with Doctor Who's idiosyncratic nature as a programme; it was difficult to classify and its appeal could not be broadly defined. Ultimately, though, this probably also sowed the seeds of its destruction, as it was only a matter of time before the BBC took the attitude that such a loose cannon eating up resources and causing 'controversy' had to be culled.
Now, however, the BBC takes an active interest in Doctor Who as a 'brand' to exploit and the limitations to the programme seem to be being imposed by the supposed 'creatives' themselves. We can see where that has got us...
Although, I do believe that Doctor Who's appeal to the imagination of children is vitally important (after all that's how we all got hooked) to write down to it as if it is merely kids stuff is deadly to its very identity.
Besides, try watching something like 'Revelation of the Daleks' and telling yourself "This is a kids show..."