I think I agree with your worry, although it seems like obesity/overweight is a much larger public health issue than EDs? For some quick back of the envelope stuff, let's take the 5 million deaths due to high bmi and compare it to the deaths from bulimia and anorexia.

https://www.eatingdisorderhope.com/information/anorexia/anorexia-death-rate says that the death rate from anorexia after 10 years is 10% and after 20 years is 20%, I don't know if this is quite the way to interpret that but let's say that of the people with anorexia, 1% die every year. I'm pretty sure bulimia is less dangerous so let's assume that 1% for both.

https://www.nimh.nih.gov/health/statistics/eating-disorders says that the overall prevalence of bulimia was 0.3% but a overall prevalence was not given for anorexia. Lifetime prevalence of bulimia was 1%, or about 3x the overall prevalence. Lifetime prevalence of anorexia was given as 0.6%, so if the ratio of lifetime to overall is the same, maybe 0.2% overall prevalence. I'm also not sure this is right, but let's say 0.5% of the world has bulimia and/or anorexia at any one time (can you have both at once? I don't think so?)

Based on the above, out of 8 billion people, 0.5% have an ED and of that 0.5%, 1% die every year. Thus, 400,000 people die from an ED every year. If these new drugs make EDs say 2x as bad but reduce deaths from high BMI by say 10% that still looks like a potential public health net benefit. And without any data on this, I'd be surprised if ED deaths rose by two-fold in response to these new drugs.

This is very rough and uncertain, mostly taking the easiest figures I could get on faith and ignoring key facts about comparing EDs to high BMI (age of death is probably different and might be ethically relevant, amount of psychological distress is probably different, I think a lot of ED deaths are from suicide and that might be particularly bad for e.g. family members compared to a heart attack or something caused by high bmi, I only included two EDs, etc. etc.), but maybe this helps get a birds-eye view of prioritization?

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As someone who was very close to a person who battled an eating disorder, I watched from up close the awful torment that her brain put her through. This brilliant person, who's now a grad student at Harvard, would literally spend an hour's effort to beat back the urge to binge-eat some ordinary thing in the refrigerator, to the point where she made me lock the fridge door with a chain, just so she could stop thinking about what's in it. I still think about her when I read about Vegovy, because her greatest wish in life was to not feel "food pressure" - and she would have awful fantasies about burning off the taste buds from her tongue, and worse. People often naively think that an eating disorder is about just wanting to get thin, and maybe that's how it is for some, but for others, it's about an unmanageable, debilitating craving for food. And that seems to be exactly the thing that Vegovy seems to help with. I know it sounds weird that a slender young woman with an eating disorder might be cured by a diet drug, but I would take the possibility very seriously.

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A lot of overeating is psychogenic, and a form of "eating disorder", or adjacent to it. Any effective means of losing weight for most severely obese people needs to address that side (sometimes it's "just" an entrenched habit of a lifetime, but often it's genuine and severe "eating as stress coping") to achieve more than medical health benefits.

Note: I'm not talking about people "overweight" by a few kg or even maybe "mildly obese".

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