The state doesn't make me pay it because I don't watch live broadcast TV, therefore I don't have to pay it. It's not a general tax it's a hypothecated tax and is administered by the BBC not the UK government.
Furthermore the state isn't in charge of administering it anyway, it's a civil matter brought about by the BBC (or rather the company which is subcontracted to enforce licencing). The BBC has the authority to do this based on the Royal Charter that governs it, that doesn't make it "state funded" or a "state broadcaster".