In the UK yes, but in the broader world the network the BBC has built up over decades gives us a lot of influence we'd never have otherwise. No matter what we think here the BBC is trusted and respected in many parts of the world.
Does that mean it should be paid for by viewers of Eastenders in the UK? No. Should it be fully at the mercy of the commercial market, equally no, that would destroy it's unique position to spread influence beyond this little island.
I'd be happy to see light entertainment supported in some way by advertising or subscription but the tricky part is identifying what is light entertainment (Is the today show? I find it so, but it certainly isn't commercialy viable). We could well find the cost of classifying output is actually more than just paying for it from taxation in the first place