Indeed, that's a dangerous path to start down. Something like 60% of the UK population is overweight: do we stop treating Type 2 diabetes because it's self-inflicted? It would save billions of pounds, after all.
Personally I think people should take some personal responsibility for the NHS's under funding. We eat too much, drink too much, don't do enough exercise and drive dangerously - it's hardly surprising the health service is struggling.
Edit: not that I'm suggesting Anorexia isn't a serious mental illness.