The licence was introduced when television sets were an exotic luxury so adding it to the tax rises used to pay for the NHS wasn't the obvious move for a Labour

The licence was introduced when television sets were an exotic luxury so adding it to the tax rises used to pay for the NHS wasn't the obvious move for a Labour government. Radio licenses existed before the NHS or most other benefits were a thing. As for why it hasn't been abolished like the radio licence... well any government that does that loses the ability to indirectly threaten it when they don't like the tone of the nation's most watched news channel by muttering darkly about how it's iniquitous funding model needs abolishing, and gets blamed for the changes people don't like.