The BBC isn't a state broadcaster in the truest sense (Pravda, NK etc) so I don't think it's a fair comparison to state provision.
As a monopoly provider and even potentially in the analogue world; the license fee made sense. In a digitally connected world where I can get just about any form of broadcast media from anywhere on earth into my home or on my phone in real time - it makes less sense.
I like the BBC' it's great value, but I can understand why some people who think it's gone beyond it's 'inform, educate and entertain' remit to become some form of moral arbiter of, or worse influencer on what they believe the audience should think, feel they shouldn't need to pay towards it.
Edited to add; as an actual tax, it's pretty regressive. To think that Gary Lineker earning his £1.5m for reading an autocue, pays the same rate as your average nurse working in the intolerable NHS can't really be seen as fair.