I did not hear the same information from others about this track, although certainly informally some areas are known for being "high burnout" such as DBT specialists, PTSD specialists, etc., and ED tends make the list. Not sure if research bears this out as higher burnout for ED than generalists? Something you might want to look into. And I'd suggest chatting with an ED specialist who works in a hospital or private practice setting to see what it's like.
What I did find in grad school and beyond was that it is really hard to get into this area without a solid practicum, internship, or postdoc with in-depth training. In many settings I've worked in, only one or two clinicians would have competence to treat eating disorders, so the earlier you can get the experience, the better. After postdoc, you're largely shut out of this specialty because jobs will require extensive experience, at least from the job offerings I saw a few years back. Ideally, if you are still early in your doctoral training, you could try to make sure you get specialist ED training and some generalist training via practica/externships.
A former supervisor of mine largely saw folks with ED in her private practice, but also worked with clients with other concerns (anxiety, depression, etc.), so she never got "stuck" working only with ED. If you have experience in generalist areas, you can always fall back on it as part of your core competence, so I would argue no, you're not necessarily shut out of generalist practice.