Government set the licence fee and legislation around it every 5 or 6 years. The last renewal put government appointed editors into the BBC in exchange for a change in Law from 'watch live BBC channels = you have to pay' to 'watch live non-BBC channels = you have to pay'. So now, even if you are just watching BBC competitors,you have to pay the BBC.. what a great business model.
Now it's also the case that you need a license to use BBC's streaming platform, iPlayer, to watch video on demand.
Note that "live" isn't the qualifier -- so long as you're not watching a feed of something that's being broadcast you're OK.
When it was first introduced it made sense to have a fee, not many people had a TV so by collecting the fee, you didn't tax the people without it. But today everyone has it, so this no longer applies.
Independence argument has some merit, but I would expect that there can be different methods that would provide the same level of independence.
The independence argument has largely been destroyed by the government itself - the last few governments have tightened their control of the management of the BBC considerably to a point where budget control matters much less.
It gradually shifted from being an independent well staffed news organization that routinely held the government to account to an understaffed RT-like propaganda outfit and huffpost-like reprinter of press releases.
