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"is the ONLY thing the Romans could not tolerate."

The Romans and Greeks practiced 'exposure' where they let the child die in the forests usually for economic or eugenic reasons. The Greeks and Romans indeed were disgusted about sacrificing children for favors of the gods. Phoenicians in Lebanon banned human sacrifice long before they were conquered by the Persians in 500 bc, while the Carthaginian breakaway colony practiced it into 150 bc.

Carthage had economic friendship with Rome long before the Samnite wars of 350 bc until after the Pyrrhic wars of 275 bc.

Reason Rome destroyed Carthage in 146 BC, is despite Carthage losing its powerful Navy (all but 10 ships), and all overseas colonies, its economy was thriving and the fear of another Hannibal being born.

This video gives the most clear concise reason on why Rome came to be the hegemon it came to be.
https://www.youtube.com/watch?v=hzyq4BXTkhQ

TLDR, the Greeks lacked the discipline to sustain a large empire based around Anatolia/Modern day Turkey region (former Eastern Roman Empire established with Constantinople in 330 AD) as seen in the fragmentation of Alexandrian Empire. Oracle of Delphi were like the CIA of today, and demanded that Rome deal with its western flank first.