why?

If you read the materials I published here you already realized that Achaemenid Empire did a really good job spreading the Indo-Iranian culture and fire worship to its provinces, which is what you'd expect it to do, that's why it's called an Empire and that's how it got so big:

It went through several major rebrandings but was still aproximately this big up to late medieval and maintained authority and absolute cultural dominance in the region up to 18-th century. Persia for Asia was like Italy for Europe. Educated people were supposed to speak Persian in Egypt, Turkey, Central Asia and India up to 20-th century. Yet we aren't hearing much of any influence of this empire on Ancient Greeks/Romans or abrahamic religions. I believe it's very easy to see, as well as some direct cultural influence on Europe through medieval. Why is that you've never heard of these? Church and religious scholars hid and denied the obvious for several reasons:

• Greeks/Romans fought Persians for centuries and hated their guts;
• idea of European supremacy since XVIII century;
• nationalism;
• admitting all the imperial eagles are just substitutes for peacocks would be so not cool;
• admitting the Latin/Greek words for God (Deus = Zeus = Theos) come from peacock ...;
• admitting animalistic idol worship in Judaism ...;
• admitting Vesta temple in Rome with eternal fire in it was a Persian temple called after Avesta ...;
• admitting Greeks/Romans and Phoenicians (aka Jews, also, given 𐘾 - celtic people?) were monotheists, just like Persians, long before Christianity ...;
• admitting fire worship origin of rituals (candles, Jerusalem holy fire) in Christian churches ...;
• admitting Europe was a colony in Medieval ...