If they don't get any income, how will they make programmes, pay announcers and presenters, and so on? Their money has to come from somewhere.
He who pays the piper calls the tune. Advertisers will expect privileges for their money, like frequent ads and product placements (Henry VIII consults his H. Samuel Ever-right water-clock. "Time for my next wife!") If they are paid for by government grant, there will be accusations of government interference, whether or not they are true.
A commercial company will expect to make a tidy profit for its shareholders. It is the British Broadcasting Corporation, not the Blinking Booty-creating Company.
If WE pay, WE get the programmes we want.