A lot of mental disorders exhibit co-morbidity with depression. When a person grows up comparing themselves to their peers, every time they fail at something that others seem to do effortlessly, they tend to think less of themselves.
Why can't I do what they can? Without a diagnosis, the answer to that question can be "because I am a failure as a human being", leading to erosion of self-worth. But being able to answer "because I have a handicap" (due to the mental condition) helps think more constructively about how to work around the handicap, rather than just expect to be able to overcome it.
In this thread, there an insightful comment that reads: it's like realizing that you are short... after decades of being told that the only reason you can't reach as high as most people is because you are lazy.
When you said "people often use it as an excuse to not work towards improving themselves", that is exactly what the author of the comment meant by "being told [that they're] lazy". No matter how much a short person "work[s] towards improving themselves", they will not get taller. They instead find ways to work around the issue, like carrying stepladders with them.
Keep in mind, that if we had never invented glasses, a huge swath of the world's population would be considered to be handicapped. And the ones that weren't, who have only experienced poor eyesight due to dust or tears in their eyes (temporary conditions, just like feeling sad would be in comparison to depression), they could very well share your attitude, and insist that people just need to "look harder".