The BBC just like any other news organization is not neutral. It sometimes leans left and it sometimes lean right. The problem is that this "leaning" is never disclosed.
If a newspaper is comfortably right-wing/left-wing and so on, I don't care about their biases because at least you know that if you read it, you are going to get a "version" of a story that fits the overall narrative of the outlet.
When it comes down to publicly funded news outlet though, their neutrality is disputable and on top of that you end up paying through your taxes for "news" that have either been downplayed or exaggerated depending on who is reporting on it.
So as a tax payer, what is there to gain from being manipulated (at best) or lied to (at worst) by an organization who is supposed to be neutral but who isn't?
I wish it wasn't the case but there has been too many stories in the past in the mainstream media that turned out to be either misrepresented or made up and there was rarely any retraction/apologies on the subject.
And just in case you think that only right wingers have problem with the BBC (for example), the accusations of biases come from the left and from the right of the political spectrum so this is a problem for everyone.
You don't seem to offer a better solution only a reason why you don't like this one.
Of course the BBC is unavoidably propaganda - even just unconsciously - that's why this Hafler Trio track from 1984 exists: https://www.youtube.com/watch?v=cIobKBy8XOs
I also have personal experience that they're far from infallible, a friend lied to them about our farcical "Potato powered" computer† and for a while their news story about this was actually available as if it was real news not a joke.
But they're clearly trying and "not good enough" doesn't seem like an adequate justification for giving up and saying we'll just go without democracy then. If this is the best we have then this will have to do.
† The worst part is that this is kinda, sorta at the edge of plausible, which is why I thought from the outset that it's not a good joke. We didn't build such a thing, but maybe someone could have or even has.