Much as I love Bake Off, Strictly, Mr Tumble (ok, not so much the last one) and my weather app, they are not a public service! Perhaps certain bits are, such as current affairs and the news.
Define a public service? Some things the BBC does for entertainment and for revenue (Bake Off is a good example of that), but how do you decide what's the public service bit? Only the bits you think are good for people? If people are enjoying it, it doesn't count as a public service?
It's funded by the public, and provides a service. It's pretty much a textbook definition. The nature of the service it provides, and whether it should provide certain parts of that service, is a matter for debate. But I find it very odd to argue that a publicly funded service isn't a public service simply because it's not 'improving'.
^These could be funded under taxation but with the same BBC charter in place ensuring it was no more political than, say, the Office for Budget Responsibility.
Broadcasting and OBR are quite different beasts. Particularly when it comes to the day in, day out provision of news and current affairs - versus economic forecasts and fiscal analysis. And goodness knows that the OBR hasn't been without accusations of bias in its short history.
We've already seen quite a bit how governments and political parties (of all colours) hate being criticised or held to account by the BBC (and other broadcasters to be fair - but few have the authority or reach of the BBC when it comes to broadcast news). Most complained about bias against them during the GE.
The Beeb doesn't always get it right - it's run by humans - but it's perceived as one of the least biased news outlets, and seems to try harder than most for balance.