Because that's what the Assyrians used. Heavy archers. Of course, the Persians also used whatever rabble they could throw at their enemies in the lands they conquered, but archery is a grand profession to have. It doesn't matter how good of a swordsman you are, even with iron armor, if you get shot with half a dozen arrows, you're dead.
The idea is to rain hellish death down on your foes until you have expended ALL of your arrows, and then you send your infantry lines to clean up what's left. The bow and the spear have always been extremely powerful symbols in the Middle East and in all of Asia. The Persians had such a bad defeat when they fought the Greeks not because of their tactics, but because Darius invaded Greece thinking everyone would surrender. It was the same for Xerxes. They invaded with a massive horde of rabble and thought that sheer numbers would scare the Greeks into defeat. They never really planned for resistance, and never really prepared for a real invasion.
But if they had, there's a very good possibility we'd all be speaking some modern form of Persian right now.