I was reading this wikipedia page:
and I thought it was strange that day-runners (hemerodromes) would have been useful to the Greeks. I guess I can see how it might be cheaper, but wouldn't you want really important news shared a little faster? Were horses extremely hard to come by at this time in Greece?
Over long distances, speed is less of a matter than endurance - and over a long enough distance, a human has the advantage over a horse. Which is not yet going into some problems with the story as commonly recounted. More can always be said on the matter if anyone would like to address themselves to it; for the meantime, OP, I commend to your attention u/Iphikrates' post on just this question.