The whole reason they are there is the mental health issue, so denying them because it's not fixed is more like denying a person with cancer any more treatments because they haven't responded well to the first 30 treatments.
A mental health problem is no more "self inflicted" than cancer is.
It doesn't really change your ultimate question though.
How about overeating (thus obsesity)?
I ask because right now the UK's NHS severely limits access to healthcare for smokers and the obese.
I think the more realistic distinction between anorexia/bulimia on the one hand, and smoking/obesity on the other -if there is a distinction in NHS's "mind"- it's that the former are more sympathetic. But I dunno, I'm just guessing. I have no idea what the mandarins at NHS and similar are thinking, or, rather, will think when their resources become even more constrained than they are now. That is, I suspect they (NHS) make choices about whose healthcare to restrict... entirely on the basis of a) scarcity / need to ration, b) how sympathetic a particular target group is. How else would they (NHS) make such choices anyways? how else could they make them even remotely palatable to the polity?
I feel like bringing up the notion of choice and free will is opening a can of black holes, but when dealing with mental illness you have to.
There are plenty of cancer drugs that the NHS will refuse to prescribe due to their expense. If you want them, you'll be told to go private. If mental health is so expensive, do we say the same thing?