I don't think anyone with ED wants to kill themselves. Where's the evidence? First of all it's mental illness so the sufferers don't exactly choose to have them, despite how angry this makes people in YouTube comments. The problem is they can choose whether to try to get better, and that isn't easy but they acknowledge they'll die if they don't get better. That's not enough for the mind to change its way of behaving.
Do smokers just want to kill themselves slowly over 50-70 years? No. It's the high, and the addiction. Smokers chose to start smoking and choose not to quit. They know they will die.
Eating a lot or not eating at all both cause highs of their own and the mental illness is the motivator. They don't want to die; they can't break free of the addiction. It's simply not that easy
I'll offer an opposite view- eating disorders are a symptom of being suicidal. This is purely antecdotal, I have no sources to back this up so take it with a grain of salt.
Of the people in known families, in my personal experience, about 1 in 3 people who were suicidal had an eating disorder. Most were also fairly young when they had ED's, as well as the signs of depression.
Of those, all of those with an ED were extremely suicidal and looking to punish themselves for simply existing. This makes sense because one of those anorexic kids is a pooner. They get addicted to the pain, and rationalize why it's deserved. I've talked with the pooner before, she rationalizes that destroying her body will give her a more masculine appearance. That's the surface excuse. In reality, she grew up in an abusive home and seems to be suffering from some kind of bipolar or personality disorder. Her brother regularly expresses concern over "him", and is incredibly protective, sonce it seems this fix is the only superficial thing they can see as helping them.
The most common places you will see this disorder are in artists, actors, musicians and models, all very high stress careers (even if successful) and are each known for an abnormally large percentage of suicidal individuals.
You have to almost not care about living if you're anorexic, it takes commitment to willingly starve every day. Even if it gives pleasure responses, the pain of it should be more than enough to make you lapse at least to a semi decent weight and fast for a couple days, not regularly restrict over the course of years until your organs are breaking down.
Again, take with a mountain of salt for my conjecture, it just seems much, much more likely to have this disorder when suicidal. Especially Eugina, you cannot look at that girl and tell me she has any desire to live. Even at her happiest, her eyes are dead.
For a small power level- for me personally, I had the disorder and was determined to not live past 23, quite a few people I knew during that time had similar goals until they got help, and then the anorexia very slowly shifted to becoming overweight (because you tend to eat more when you're happier) this would cause a relapse, people would stop the medication, and the anorexia would come back.
(This might be confusing to people who also never had depression or known someone very well with it, they tend to search out others with depression or depression-like tendencies, common markers to look out for are putting everyone else above themself, stretching themselves to help others to their detriment, becoming reserved or "off" for days at a time, then regularly not responding, or seeming to respond like a robot with short, simple answers. You may not notice this if you aren't close, they're very subtle and will do their damnest to hide it from even the closest of friends. They will also regularly over work themselves with excuses like "oh I just need the money", "I like being busy", "they need the help". Finally, you won't hear them talk about their life very negatively very often, and when it slips, it's only complaining. This is usually in the midst of a depression episode where they see no good in the world. People with severe depression are very guarded about letting anyone know what they're actually feeling or have an opinion on, but are very good at redirecting to a different topic. They'll often turn it around to ask how you're doing or what's going on in your own life, or talk about someone elses life instead of their own.)