Preventing illness also falls under the umbrella of health care, at least where I live.

"Preventive medicine" get's you doctors who do a lot of mammograms and then operate people who don't really need an operation.

And even if it didn't, it's still clear what (most) people mean with the word even if the word doesn't mean what you want it to mean.

If the word had no meaning there wouldn't be much gained by abolishing it.