I wonder if technology is also a factor: as I understand it, and I may be wrong, one difference between the BBC and the likes of Netflix or Virginmedia is that the latter two require satellite dish/cable/internet and/or a 'box' to access the service, without which (or if you forget to pay) there is no access, whereas the BBC is transmitted so that it can still be accessed using the older aerial technology.
Therefore, it is probably more comparable with ITV/C4 - which raises the issue of the BBC accepting advertising, and if that was an option there would then be an impact on the income of these other commercial channels. Then there are the issues of taste and content, along with the extent to which the BBC would thrive in a competitive commercial environment.
I'd have to say the best things about it for me are BBC4, its website and the 'Sounds' app: there isn't that much on its flagship BBC1 channel that interests me.