Yesterday, the BBC's website declared that the news the USA had been listening in to the phone calls of German Chancellor Angela Merkel had led to "the worst diplomatic crisis between the two countries in living memory.

This will come as surprising news to the 9% or so of the UK population who were born before America's relationship with Germany took a turn for the worse in December 1941. It may even surprise some younger people who may have noticed that the final peace treaty with Germany was not signed until 1990, and the USA and the DDR weren't awfully chummy during the previous four decades.

All the same, I don't think it's indicative of BBC bias, any more than I think the ill-judged insinuation that Prince Harry might have taken cocaine - made on the satirical news show Have I Got News For You - is an argument for shutting the corporation down.

Of course, like almost every large public body, the BBC is biased - indeed, it is so hand-wringingly liberal, and desperate to seem unbiased, that every so often it acknowledges that it is biased. My own view is that it's not very useful to describe its prejudices as left-wing, though; it is more that they are metropolitan.

It tries awfully hard to be politically correct. There is a stated aim, for example, that 12.5% of BBC employees should be from ethnic minorities (which is 4% higher than the population at large), yet Greg Dyke, the former director-general, described it as "hideously white", while the television critic Victor Lewis-Smith noted that in practice, equal opportunities meant the BBC canteen was full of "white people eating, while black people cleared away the plates".

Its agonising over its own shortcomings has reached new heights since the revelations about Jimmy Savile, the corporation's spectacular mishandling of the reporting of those revelations, and then its even more spectacular mishandling of its reporting on the mishandling… well, you get the point. Then there was the criticism of the National Audit Office over the BBC's pay-offs - tens of millions of pounds-worth - to managers.

Against that background, it is fairly unremarkable that the chairman of the Conservative party, Grant Schapps, should have said he is considering whether the BBC should continue to receive the same level of funding from the licence fee after its Royal Charter expires in 2016. It's just as predictable that the response of a BBC spokesman should have been that "transparency is key to the future of the BBC. So is its freedom from political pressure."

The fact is that the case against the BBC's current status has nothing to do with press freedom from political regulation - unlike, for example, the very real dangers in the Leveson proposals. Although other media organisations, such as Rupert Murdoch's newspapers and the Daily Mail, appear for both commercial and ideological reasons to be engaged in a vendetta against the BBC, that need not be a point either for or against the corporation. Even the fact that the BBC is - on any objective measure - often biased (something which, to be fair, could be said of any large institution) is not the chief case against it.

The reason something will have to be done about the licence fee is that it has become an unjustifiable anachronism, and one that may very soon be unworkable, too. That's got nothing to do with the BBC's intrinsic merits or failings. It is merely a consequence of the ways in which digital technology has completely swept away the traditional ways of consuming media.

A lot of attention has been paid to how that has affected newspapers, but the changes in broadcasting media have been every bit as significant. Think, for example, of the latest critically acclaimed American series, Breaking Bad, which I happen to agree may be one of the best things ever produced by the medium. It wasn't even shown by a British TV channel, bar a brief, cancelled, stint on (I think) 5 USA. Almost everyone who watched it saw it through Netflix or on DVD.

Only three decades ago, there were three television channels. Now there are hundreds. Even Channel 5 isn't content with one channel; there's 5, 5* and 5 USA, not to mention the +1 and HD versions. No-one even needs a television to watch it; indeed, broadcasters are going out of their way to provide access to their programmes online, or through catch-up systems like the BBC's iPlayer. Radio programmes feature callers who are (for unfathomable reasons of their own) listening to Jeremy Vine on the beach in Thailand.

Whether you think the BBC provides good value for money in exchange for the £145.50 tax on owning a television is irrelevant, because it's very easy to imagine that television, as we currently have it, will soon cease to exist. For quite a lot of people, the only reason for watching television in real time is to talk about it on Twitter - indeed, some programmes are greatly improved if you only follow the Twitter commentary, and don't bother watching.

The majority of the BBC's audience for its website - the world's largest news website - pay nothing at all for its content, since they don't live in the UK. Yet while this is clearly unfair to every commercial operator, the BBC can employ 8000 journalists. At the G8 summit in Northern Ireland, one in every three journalists was from the BBC. Two years ago, the corporation sent 263 people to the Glastonbury festival, and had 250 covering one event marking the fact that the Olympics would be starting a year later. The director-general gets paid three times as much as the prime minister - and that's after the salary was cut by £220,000.

Yet the fact that everyone could legally access the majority of the BBC's output without paying the licence fee, if they swapped their television for a computer monitor, makes all this duplication and expenditure utterly unsustainable. The upheaval that has already taken place, and is continuing, in print media will be replicated in broadcasting; the BBC cannot imagine that the peculiarities of its funding model will exempt it from the challenges that will follow.

For those who work within the BBC and anyone who values its output, there is no point in pretending things can continue as they are. But if a case is to be made for the BBC as offering something distinctive and valuable, it urgently needs to address these issues. First and foremost, that means asking what the BBC is for. If, as the corporation's managers seem to imagine, it is for taking the moral high ground, the public is entitled to wonder whether it's making a good job of that role, and whether it's worth £3.6 billion of public money.