I think this is just a comparison between roman and italian stereotypes given to us by movies, literature, culture... but not necessarily realistic.
People who killed their relatives were mostly the high ranking politicians and power-people, you know, the kind that get books, and novels and plays written about them,
these are people who are more similar to today's mafioso families ( who may kill family members for power gains, or adopt people as 'made men' )
Regular ancient peasants mostly lived like peasants have lived for millenia - and they couldn't easily own slaves, or get away with murder like rich people do even today.
Roman empire is an example of how a state with institutions can be a superior force, especially in a world where rarely anyone else has a complex and branching governing system.
Everyone in Europe wanted to be Rome, they copied Rome, and when they clashed with Roman culture and institutions, the barbarians would learn the lessons that it's smarter to emulate Roman institutions and settle down.
As for the military power - Italy as a province couldn't compete with other Roman provinces. Even when it comes to commerce and development, they were hogging resources from the rest of the empire for several centuries,
until they became essentially a backwater to some more geographically advantageous cities like Constantinople, Alexandria, Antioch... ( Constantine was just one of 17 Roman emperors born in the Balkans, this doesn't account for emperors and powerful men born on other locations, Romans who conquered Italy by political or military force, not because Italy was an essential part of the empire, but because of its traditional role. Constantine for example didn't really care about the city of Rome, and didn't even meet with the senate, thus displaying how insignificant these old places were in a new Roman world which gravitated towards the east ).
Even in the fabled days of Caesar, the riches and military power of Pompei lay in the east. Pompei just got outmanouvered by Caesar several times, but if history went some other route, and Pompei was at full force of his eastern legions, he'd have won ).
So, my point is that Italy, even in Roman times wasn't a geographically important location for building an empire around the rich parts of the mediterranean. Even before the barbarians it was invaded and laid waste several times by Hannibal, soon after that Rome almost succumbed to Cimbri and the Teutones ( a barbarian invasion 600 years before the fall of western Rome ), and then a series of generals, would-be emperors and emperors succesfully conquered italy.
On the other hand, you forgot about Venetians and their dominant role throughout the medieval era and the mediterranean. They were a sort of empire in a new world where trade was more lucrative than outright conquest and occupation.