Can real German speakers tell me if "Leiter" was always a very common word for this usage or merely a not-unreasonable word that won out post-war because it happens to be a bit like the English word? (In fact I suspect they are cognate, maybe that's why electrical conductors are sometimes called "leads").
Führer and Leiter seem similar in meaning, but are really quite distinct, both in denotation and connotation. And, contrary to what grandparent poster said, Führer is by no means dead.
"Führer" means guide. As in, a mountain guide ("Bergführer"), tourist guide ("Reiseführer" - both guide book and person), or driver of a vehicle: driving license ("Führerschein").
Similarly, "Anführer" is a leader of a like-minded group, often in the sense that he is not a formal leader. To pick an example from current affairs: Carles Puigdemont is (formally) the president of Catalunya, and (informally) the leader ("Anführer") of the independence movement. There is quite a number of words derived from Führer.
The verb "leiten" means to direct. Thus, a "Leiter" is somebody who gives directions: a director. This was, and is, a reasonable word, especially in a professional context.
To explain the Nazi diction a bit. Think of uses like Bergführer ("mountain guide"): somebody who leads his charges skillfully through treacherous terrain. I suppose that was the kind of image the Nazis wanted to project on Adolf Hitler (who you are of course referring to). It's true that Führer may sound politically piquant to German ears, but only in quite specific contexts. It's a pretty normal word.
But I still sense there is a post-war avoidance of the word: to you it might seem very common but I hardly ever heard it except as part of a larger compound. Compound words are so common in German, that the omission might not be obvious to people who are too familiar with it.