I think of self-awareness as a skill one can learn, cultivate. I believe that we can't have too much self-awareness. Could you have too much of any ability, like physical strength, logical thinking or rhetorical skill? Abilities aren't bad or negative in themselves, it matters how one uses and cultivates them though.
In the case of self-awareness it is just one part of a mental development. If there is a problem when cultivating it like depression there should also go some consideration into why one is depressed.
