The most recent example was this morning on Radio 4. An artist was talking about using her art to "help people with mental health, because they can be forgotten". I hear it all the time. "She/he's got mental health" when referring to someone who is mentally ill. It would be different if they said "she's got problems with her mental health" but they don't. I've had lifelong depression, so I would love to have mental health, but I haven't. People wouldn't do it with physical health. If someone's physically ill they're not described as having physical health are they?
Btw, apologies to any pedants here who notice grammar and punctuation mistakes. I posted here because it seemed the most suitable board on MN to post about this niggle and I wondered if anyone else has noticed it happening.