Wars in more recent times are less impactful on the American populace. The last war that had a significant influence on the average person was Vietnam, and even then, we almost had John McCain, Al Gore, and Wesley Clark as presidents, although none were particularly high-ranking in the military.
After being West Point valedictorian, Wes Clark was NATO Supreme Allied Commander, Europe – can’t get too much higher than that. But yes, McCain was “only” a Captain, and Gore served for a year or so.
That's true, my mistake, and I guess he was in charge during Kosovo. But I'm not sure he would really count as being a "military leader" in the same way that Washington, Grant, or Eisenhower were.