I commented elsewhere, but Roman culture was distinctively not Greek. The Romans valued virtue, filial duty, martial strength, etc. While the Eastern empire gradually became more "Greek" (in the same sort of cultural syncretism which "Sinocized" the Ming), this wasn't true of the Romans as a whole.

The Goths in Rome explicitly modeled their state after Rome, to the point where they considered the Western half to have survived. The organization of early Frankish kingdoms is a direct result of Roman estates, as experienced administrators were all... Roman. Rinse and repeat. It's not so much that it "informed" their institutions as that dux->duke, because they were the same position, and Diocletian's dioceses obviously survived as organizational units, along with Diocletian's organization of the empire (of which feudalism is a direct result).

During the Renaissance, ideas of liberty and democracy aped the Romans, but none of this was a cargo cult, as the ideas spread in the Renaissance drew directly from Roman historical sources (including arguments for why they did/did not work) rather than any cargo cult mythology.