The funding makes sense for the times for when the BBC started, and started making a lot less sense at the turn of the millennium. The licence fee is an outdated way of funding public service media.
I'd advocate for a public service media fee, levied on Internet service bills, streaming media subscription bills, and Internet device purchases. Maybe even impose a fee on Internet companies who make it possible for people to livestream.... after all a livestream fits the definition of a live TV programme, something which you presently need a TV licence in the UK to watch.
I'd give the BBC a lot more commercial independence, maybe even splitting it up more, and funding present day commercial broadcasters like ITV and Sky to produce public service programming.