Any country with a state broadcaster, the public pay for it somehow.This day and age there is no reason or justification to charge people to watch a television, very surprised it has not been kicked into the dirt.
The idea behind the license fee, is that it removes a large amount of potential pressure from the current government by the government not being able to (threaten to) change the funding at short notice.
Without the license fee, a lot of programs wouldn't exist.
You might not like a lot of the content, but they probably produce something you do/would watch/listen to, that wouldn't be justifiable without subsidy.
How many private companies would commission things like the often well regarded nature documentaries?
Or do you think the high standard of media production, be that TV or Radio, would remain as high if it was a commercial race to the bottom?
And for those who want to complain about Dr Who, that's one of the programs that would still exist without subsidy, as it's one of the BBC's most profitable shows that they sell abroad (just like Top Gear was, until they killed it), so it actually reduces your license fee.
However the world of media is always changing.