I believe most, but not all, Britons DO understand that "public sector broadcasting" is a "good for all society". I've not seen the petition but it sounds like this was a debate on how it's funded not whether it should exist. So understanding the value, but thinking it is an inefficient funding method requiring it's own system and persecuting those without a TV with surveillance and demands they get a licence, the desire is to keep public sector broadcasting but do away with the obnoxious tax.
And who on Earth is suggesting other broadcasters pay for it ?
It's a public good, provides for those unable to afford other entertainment, and provides the world with British views, culture, etc.. The sensible and cheaper way to collect it's funding is clearly through general taxation.