It sounds rather odd really for no one really notes that anything does die from opportunity costs. But I think that it might well be possible that that's what does in the BBC in the end. I'm prompted in these thoughts by Bill Quango. He notes that it's becoming less unusual for people not to have a TV. And that even those who have them seem to use them less than in the past:

I have been monitoring my own recent TV use and its dismal. I'm struggling to watch programs I actually like. TV seems to have become old hat. I now watch less than 10 hours a week. I listen to far more radio than Tv.  At least twice as much, maybe 3 times as much. Mostly because its easy to combine with other activities. I listen to music as much as I watch TV. In fact I pay video games more than I watch TV. I certainly use the internet far far more than TV use.
 
And that is the root of the TVs demise. There are other things to do. And they are now easy to do. Read a book direct on download. Multiplayer mayhem {wars of the roses- a current fav} All night shopping. News. current affairs. Gossip. Politics. Youtube. Facebook. Twitter. And general mooching around.
 
As there are more ways for us to pass our time then the cost of doing any one of them rises: for we're giving up more things to do that one. As the costs of something rise we're not all that surprised that people do less of it. You might not believe it but this has been used as an, in part, explanation for the falling birth rate. There's so much more to do in life than only have kids these days.
 
Of course, I think it will be a long time before the TV really goes the way of the pianola. But the BBC itself is in a precarious position long before TV itself dies. As TV becomes less central to the leisure life of the nation then a tax specifically to pay for it will become much less politically tenable. I wouldn't be at all surprised to see in a decade or so that support for it just simply dies out.
 
Killed by opportunity cost: there's simply so many other interesting things to do these days.