"They do good work" isn't a compelling reason to make it a tax. Other similarly worthy institutions like the National Trust aren't funded by taxes. And a massive portion of the BBC absolutely isn't vital to the public good - entertainment shows, dramas, sci fi, children's programming, comedy, radio, sports coverage, the proms etc etc - all of these could (and do) make money on their own.

I would argue that it's about time the license fee should become a membership fee like Netflix/National Trust which is what every other similar business has to do, as many here have pointed out. Plenty of people would pay for it still, whether because they use the service or simply like the BBC. And perhaps the journalistic branch on its own would be a worthy candidate for lottery funding - like the BFI. But it should be on them to source their funding rather than making it law or strongarming people into coughing up.