What's wrong, I think, is that when it comes to paying for the Beeb (which by virtue of its size will be unable to find a single citizen who likes everything it produces, and yet probably produces at least some service that could be of use to any individual) a lot of people suddenly have a fit of Galloping Libertarian Farquar Syndrome, and because The Powers That Be continue to pretend the licence fee isn't a tax, they then fume about being forcibly made to pay Not-A-Tax for something They Don't Want.
I don't have kids, and I don't own a car. Money from my tax contributions goes towards both those things, and I'm happy for that to be the case because I understand the greater social good that comes of having such infrastructure in place. (Aside from anything else I can see what's happened with the UK rail network since the Tories decided privatisation was awesome and flogged the things off...which, in its own way, is a great argument in favour of the licence fee).
The Beeb produces enough services and creates enough public-interest content that its existence requires no further justification, in my opinion. Someone not wishing to avail of them should be paid no more heed than someone saying that because they're not sick they don't want to have to pay any tax towards the NHS.
I can give you an even starker example of why the Beeb is actually a %^&8ing good deal. Ireland has a television license scheme, and it's much like the UK one. The state broadcaster does *not* have a no-adverts policy, and its home-produced content is largely crap. This is at least partly an economies-of-scale issue, but it usefully serves as an alternative example of what *could* exist in place of the Beeb.