Around 2000 years ago the city of Rome had 1 million people.

Even 8000 years ago human beings were not so distributed that they never encountered strangers. There were a few proto-cities back then with ~1,000+ people, which is enough for strangers on a regular basis.

> Around 2000 years ago the city of Rome had 1 million people.

And then as now, the urban population was not even reproducing at replacement level. The population of first-century Rome left zero genetic impact on Italy.

It was less of a problem then than now, since the urban population of the distant past was a negligible percentage of the total, whereas for us it's the majority.

> The population of first-century Rome left zero genetic impact on Italy.

A million people left no genetic impact? Are you sure about that? Seems too far fetched even for an exaggeration.

The genetics of modern Italians show absolutely no trace of the immigrants we know were present in Rome. Any impact left by the population of Rome was indistinguishable from the existing genetics of the Italian countryside at the time, but we know that the actual population of Rome was very different from that of the Italian countryside.

From a genetic perspective, cities are just somewhere you go to die.