The same reason it costs me some £40 a month and a further £30 every 3-6 months just to be able to see further than about 10cm in front of my face. If I don't have it, I won't be able to find my way to the other side of the room, and that's tough luck.
There's all the more reason to pay for braces, since they're optional. Plus, once you're a grown adult your teeth will take forever to straighten, so it would cost the a lot NHS more.