I'm not sure why the BBC don't just make it a subscription service or sell their programming to Sky and/or Virgin and add advertising.
For one thing it's not the BBC's decision...
The BBC operates under a Royal Charter as approved by government and under the guidelines enshrined in the charter.
That includes some very strict limits on what it can or cannot do (IE it cannot have more than something like £100 million in debts*).
The terms of the service they provide (IE the well known "educate, inform, entertain), and how they provide the service - for example they have to provide content on a non favoured basis - so they have to make the same offer of content to all the platforms, be it putting the channels on DTT, Sky, Cable, or making the Iplayer available on all the consoles under the same conditions (IIRC the xbox version was held back at one point as MS wanted it in the gold package, the BBC would not have been allowed to agree to that).
And finally, the way it's funded is set by the government.
Strictly speaking the TVL doesn't even go to the BBC, the BBC are empowered and required to collect it (using the same methods the post office did for decades before), but then it goes to the government.
The government then pay the BBC most of that back as part of a pre-agreed amount (increasingly hiving off parts of the TVL for other government projects such as BB, and to pay for the World Service - which used to be paid for by a foreign office grant).
*One of the reasons they've had to basically lease their new studio complex at Salford was because they could not under the terms of the charter put together enough money to build a new one themselves (it's a billion pound+ investment). And it's worth remembering that the BBC lease the Salford facilities next time you read some garbage in the papers about things like "BBC offering staff escorts to train station" or "BBC waste money on faith room" - both were offered/provided by the site management to all staff regardless of if they were BBC, ITV, Sky, or whatnot
