"You playing console games doesn't provide that which is why there is no console tax."
Many of us do not believe the BBC provides what you say it does, it is not independent, especially from politics, because the charter comes up for renewal every now and then. Also it is not a public good because everything the BBC does can and is provided by private sector businesses, and I am excluded from watching it when I don't pay the licence (as I don't).
You may prefer the BBC but it isn't a public good. That argument is about 50 years out of date (since ITV started anyway).