Why did the Eastern Empires used Archers a lot more than the Western Empires?

An interesting question, which got me thinking. After a little bit of reading, I get the idea, that archery got first developed as a successful type of combat in Eastern countries, along with Hungary and Crete. There it got perfected and was a part of the peoples' culture. Roman armies didn't train archer units, because they were comfortable with their current military tactics, which were quite successful. But as their empire grew bigger, they took over many of the arcer nations, so they began using batallions of archers together with their usual armies. Archers were, however, never really their thing, they never were a part of Roman culture and Romans just didn't have high regards for it.