One of the problems I see with "hearing impaired" on a larger level is, that it was meant to be a "PC" term - "nice way" of saying something that hearing people and the medical establishment actually think is a problem. Playing with "nice-ities" without actually looking at broader sociological implications is a way for a majority group to retain control. That mindset perpetuates the idea of d/Deaf as disabled, lacking, lesser than. This also perpetuates the disregard of sign language as valuable language in deaf communities and in general.
That said, no issue with people choosing what to call themselves as individuals.
But I think there are larger group dynamics around terms and to think that "hearing impaired" is "just a term", negates social and political ramifications.
I also have dyscalculia and various processing and motor issues. My LD happens to be something I have - but not something I am.