I have a vague memory of a short-short story (one page, maybe two at most) about a scientist who develops a cure for cancer. His boss tells him the discovery had been made and suppressed, because cancer was one of the few things left keeping the population in check. The scientist protests, "But I have cancer!" and his boss replies "So do I." It might have been an Asimov story?
'The System' by Ben Bova. Can be found in '100 Great Science Fiction Short Short Stories'. Isaac Asimov was indeed one of the ones who helped compile the stories and was the biggest name on the cover, so that's probably why you remembered him most.
"No. Not cancer. Cancer stays. Demographic analysis knocked out all thoughts of using the cure. There aren't any other major killers around anymore. Stop cancer and we swamp ourselves with people. So the cure gets shelved."
For a stunned instant, Hopler was silent. Then, "But... I need the cure!"
Gorman nodded grimly. "So will I. The System predicts it."