I suspect it's a leftover from the earliest days of broadcasting. TV and radio were rare novelties, so telling the 90% of the public that didn't have one yet that they had to pay tax money to support the BBC would have been infeasible.
It's interesting that in the US, there was a significant link between the broadcasters and the hardware manufacturers-- General Electric owned NBC for many years, and DuMont had their own network. I wonder why this didn't take off in Europe, with the airwaves dominated by a "Philips channel" or a "Thomson network"?