CHICAGO—On the September day that shooting began on Dick Wolf’s “Chicago Med”—his third TV series to launch here in as many years—the producer delivered a pep talk to the cast and crew. He stood behind a bar lined with bottles of prop booze, a set shared by all three series, and said, “My fondest dream is that most of you here will retire from this show, and your kids will be on it.”

It sounded like an absurd hypothetical—except that Mr. Wolf had done it before.

Twenty-five...