We choose whether to read or watch anything owned by Murdoch or anyone else. If we wish to watch any other live TV we have to pay the BBC tax. That's where it is different, wrong and beyond any justification. Whether it is or isn't good value or biased doesn't even come into it.
I hear and understand with what you are saying, which if I read right is: "if i don't use the service, regardless value, why should I pay for it?"
From my limited understanding, there is the choice not to use it and therefor not to pay for it by simply telling them you don't watch live tv.
Technically it isn't a tax though - this is an important distinction. A tax is mandatory, a licence allows you to opt out, which you can. That is a good thing about the licence.
If the licence was centrally funded by tax, it would make opting out of it impossible. And people would probably get worked up about it more (rightly or wrongly) as they'd feel it isn't good value or that they don't use it.
Ultimately I see the gripes around bbc and how they are being funded as purely academic argument around payment method. The underlying issue is that people don't want to pay it because they don't use it or think it's a bad service. Any public service is like that and will always be like that. The alternative is either full privatisation or a user pays system, which will introduce horrid advertising and introduce further bias, making the public service worse for all. With the licence people do still have the choice.
If the discussion is around the payment, it invariably relates to a persons perception of quality and value of a service, and whether it is worth the price paid. The "bias" of the news service as what people factor consider when measuring quality and value. They are all kind of linked together.
I think the problem overall is very hard to answer fairly for everyone, the current solution isn't ideal, but then on the other hand all other solutions introduce other types of problems which are just as bad. It seems like maybe the licence is the best of all the bad potential solutions, and is fair enough for the majority of people.