I still don’t understand why the tax payers in the UK would want to support the BBC
I don't think it's a question of want: the BBC is PBS after a fifty-year steroid and HGH regimen.
There isn’t much ‘want’ involved.
Owning a television requires a television licence (as they spell it). The licence fee funds the BBC. There is always political pantomime about the amount of funding but the mechanism remains - and there is even an enforcement arm with all manner of Orwellian equipment to scan for ‘unlicenced’ televisions and punish the offender.
With this setup it’s easy to see how one hand washes the other.