I’m with youngmaf, sp, and I suggest you are mistaken when you say that TV licence fee money goes to support cable infrastructure. Mine is with BT and I am absolutely certain that no cash comes their way from the TVL and I believe the same can be said for Sky (who mainly use BT’s Broadband infrastructure for their internet provision anyway) and Virgin.
If the government decides that the BBC exists for the “greater good” of the nation as you seem to suggest then it should be funded from general taxation (where, as bad as the taxation system sometimes is, at least some cognisance is made of ability to pay). There are lots of things that the government recognises as for the general good of the nation (e.g. the NHS, the education system) where people would not pay individually in the form of a “user fee” if required to do so. If the BBC is seen in a similar light it should be funded in a similar way. If it is not considered as such then a fee should be payable to watch BBC but that fee should not be payable by those who do not wish to do so. The TVL fee in its current form is not a fee to watch BBC output, it is a tax to allow people to watch television (whether they choose to watch the BBC or not).