The TV Licence is not a "tax". It is not collected by Government then spent on a public service.
It's collected by the BBC directly by their own vehicle, Capita
Normal, reasonable people have no issues whatsoever with tax being collected to pay for public services they do not personally use, but which still benefit them indirectly, schools, and suchlike, because they accept it's a worthwhile and necessary investment which has benefits for their communities.
The BBC is in no way comparable, because it's main M.O. is to produce content for the purpose of leisure and entertainment, and it's also not a monopoly in the way most public services are.
If you desperately want Televisual output to consume, there are plenty of sources of that other than the BBC. There are few alternatives to most public services, so people accept that as part of the contract with the State they'll pay tax and receive a service in return. There is no need for such an arrangement with regard to a broadcaster, because most people can cope perfectly comfortably without such a thing in the first place, which is why there is no argument for a compulsory tax to fund an entirely non-essential service, one that millions of people in the UK are already managing perfectly well without and have long since moved on from.
It's not remotely similar to the NHS, or Education for example, where people absolutely do have a need for healthcare and do have a need for children to be educated, because the "alternatives" to those are cost prohibitive for most people. It's precisely the opposite with the BBC, in that it's the Licence Fee which is exorbitant compared to some of the alternatives, and given that it is an entirely elective non-vital service, the notion of being "taxed" in order to fund it instead, whether you use it or not, is utterly indefensible.
So yes, the fact the BBC is the State broadcaster is completely and utterly irrelevant, and the fact you personally are happy to fund it in no way justifies foisting that tax on people who have absolutely no need of a "State" broadcaster, do not use it, would not miss it, and also have plenty of other more affordable options which do the same thing or better.
The BBC needs to start operating in the real world, and the fact it references "competitors" itself but refuses point-blank to entertain the notion of "competing", instead continually relying on preferential treatment by government, is a farcical state of affairs which needs brought to an end.