You pay tax when you go shopping at Tesco or Morrisons, you don't complain where it goes, it doesn't go to Tesco or Morrisons, the tax goes into the general taxation pot
You pay a tax to watch live TV (or stream on iPlayer). That the money goes to fund the BBC isn't that relevant, apart from you know where the money goes
You pay a tax to drive a car, it does not go to fix the roads, it goes into a general taxation pot
If the TV Licence didn't go directly to the BBC and went into the general taxation pot this line of argument wouldn't exist.
Taxation goes to run the country, in theory for the benefit of all (yes lol), you and I only get to (sort of) say where it gets spent when we vote for people at a general election
You using the BBC isn't relevant here, I presume you aren't unfortunate enough to be homeless, a very small part of your taxation goes to fund help for those people, maybe you shouldn't have to pay that because you aren't homeless.
A fully functioning democracy really should have an independent state broadcaster, whether you choose to use it or not is up to you but you do need it to exist for the sake of the democracy that you live in. WIthout it..... well, look across the Atlantic.
Again, it is not a con, there is no confidence trick here, apart from you fooling yourself that you don't need the BBC