The Romans of the same time period (200’s-100’s BCE) conquered Carthage and Spain, but other than the gladius and a navy, the amount taken from those cultures pales in comparison to what the Romans got from Greeks.
You answered yourself in the question: it's because of culture.
Greeks had a large cultural baggage to show to Romans, much more than Etruscans or other populations: they had literature, arts, maths, sciences.. Romans liked to respect other cultures, and in front of the magnificent of the Greek culture they only could absorb a lot of practices.
However it must be said that it was long and hard to let the Hellenic culture break into Romans hearts: Greeks had some colonies in the Italic Peninsula in the IV sec. B.C. , but the Hellenic culture started to spread only in the II sec. B.C., after the Roman expansion in the Mediterranean sea. A lot of slaves were brought to Rome, and some of them were men of culture, that Romans used to instruct their children.
I suggest you to read something about the "Mos Maiorum" and the "fight" between Catone and the Scipione family.
By your profile I see that you like Romans: read some books of Alberto Angela, one of the best documentarist in Italy.