Ailchu, I don't want to take the thread off-topic again, so I'll be brief. Yes, there is a distressing gap in the data in this paper of virtually the entire Bronze Age, but we know there were Indo-Europeans in northern Italy at that time in the form of the Parma Beakers.
We have Beakers from Sicily which don't have very much if any Indo-European, so I don't know what precisely the data will show for Southern Italy. However, we know that there were Italic tribes there, tribes which would have been a mixture of the original Italic speakers entering the peninsula who then moved south, but then there was, from what we already know, also a Bronze Age migration from the Near East which hit the South Balkans, Greece, and presumably Southern Italy. In addition to all that we have the Greek migrations of the first century BC, who would probably still have been pretty Mycenaean like. Also, you seem to have forgotten the genetic make-up of the Mycenaeans. The people of whom the Iliad and the Odyssey recount legends may have had an Indo-European language and social structure, and horses and chariots and a war like mentality, but they were mostly Anatolian Neo and CHG/Iran Neo. Their steppe percentage was extremely small, much smaller than that of the Iron Age people living around Rome.
You can look all this up. It's all in the papers. I'm writing in haste, so if I've make little errors, I hope people correct them.
As for inter-marriage, it's true that Rome was a "stew" of different peoples for about 400 years, and New York City and London only for about 100-150 years. It's still a considerable amount of time.
There is extremely little intermarriage in New York between blacks and whites and between East and South Asians and whites. (I'm using "whites" for people of European descent.) Up until the time when I was in university, Jewish parents were still sitting shiva for children who married "gentiles", and they were second and third generation. I knew and know people who were in that situation. Yes, it has changed, but only because the Jews have given up on a lot of the parts of their religion which kept them apart, i.e. eating only kosher, ritual baths for wives, doing absolutely nothing on the Sabbath, accepting the children of a gentile mother as Jews. That all came about because of the Reform movement. That is completely contrary to the situation in the classical world. Yes, as I explained in another post, there was a movement of Jews to assimilate to Hellenistic society. The Sadducees are an example of that. So is Philo of Alexandria. However, the increasing polarization pushed by the Zealots, and then the Roman Jewish wars, meant the ascendancy of the Pharisees and the most restrictive type of Judaism. They turned inward and closed off contact with pagans and Christians both. For a gentile who wanted to convert, he had to undergo adult circumcision, and say goodby to any advancement in the Roman world. He would also be subject to the periodic purges of Jews from Rome throughout the time of the Empire. The majority of the Jews, who were indeed a large part of the population of Rome and other mercantile, port cities, who blended into the "Roman World" most completely were probably Jewish Christians, but even there they were marginalized and forced out to a large degree. If you want more information, the best original source is "The Acts of the Apostles". Constantine and the later Christian Emperors were, in our understanding of the word, Anti-Semites, and laws prohibiting the marriage of Jews and Christians were quickly enacted. So, in addition to the Jewish authorities in the Imperial Era prohibiting inter-marriage, by the end of the Empire, the Roman Emperors were prohibiting it as well.
For the third time, you just have to look at what happened to yDNA "J1". It virtually disappeared.
Now, does that mean that there wasn't some intermarriage between "locals" and people from these foreign enclaves? Of course not. I'm sure there was some, but unless they had the money and resources to move away to the east and the safer Eastern Roman Empire, they died in those cities of plague, hunger, or just as victims of war.
My people lived through the destruction of their cities. We know what happens. Look at Germany itself as an example. You think that after World War II people from the East didn't fill in the areas in western Germany that had been devastated? Or how about even before that after the religious wars in Germany. History repeats itself.
As for England, this is what the data shows:
In 2001, 2% of all marriages in the United Kingdom were inter-ethnic.[411] Seem like a lot to you?