Some people are moderate about some things because they care more about other things.
In the 1940s, Churchill was a moderate on domestic policy because he knew winning the war was all-important. Eisenhower was a moderate on many domestic issues because he thought the Cold War was more important. They benefited from the fact that a lot of the things we argue about now weren't real issues.
But it's like that with most politicians in power. Reagan didn't pursue his domestic agenda aggressively because he also cared about the Cold War and made winning it a priority. And Reagan wasn't as strident about foreign policy as some of his critics wished because he sensed that the Soviet Union would crumble if we stood up to it. I'm not saying Reagan was "a moderate," but even he had his critics on the right during his time in the White House.
You can despise moderates if you like but they do have the vote and enough of them do show up at the polls to swing elections one way or the other.
Churchill and Eisenhower would be called “radical right wingers” by the NYT and their ilk today. Back during the days they held office, the ideas of legalized abortions and marriage being defined as anything other than between one man and one woman were unthinkable.