The romance languages formed due to the legacy of the Roman empire, so their success is largely due to the Roman success. People say that the roman empire ended, and while indeed Rome lost its central role in many ways, the roman empire's legacy is still felt. Before the Romans though, there have been the greeks as well as the hittites, both speaking indo european languages. Romans pretty much copied a lot of greek culture as well as their strategy of building trading outposts everywhere.
I think a similar argument can be made for the legacy of the indo europeans. You just have to go a bit further back, before greek and hittite and celt and iranian/aryan and vedic cultures where a distinct thing, there was one single culture speaking a single language: the proto indo european people and culture. They had a lot of success (horse drawn carts with wheels, bronze working). They slowly spread east and west and slowly diverged for several millenia until we reach the time frame you were talking about. Those descendent cultures didn't branch and stay isolated forever after; as you correctly point out, they did influence one another again and again in successive waves.
The original question in this thread was: why was PIE culture so successful that it supplanted almost all existing PRE-indo-eurpean languages. Vascon and Etruscan survived (and possibly others), the former evolving into modern Basque, and Etruscan slowly dying out (very likely by the end of first century AD there were no more etruscan speakers)
The steppe people evolved to raid and invade agricultural communities; and those communities evolved to grow larger to fend off the raids.
"pressure from the steppe selected for the unification and scaling-up of agricultural societies into larger groups to more effectively counteract these incursions. This in turn would select for greater size in pastoralist communities, and also other neighbouring agricultural groups who were now relatively smaller and at a competitive disadvantage with their neighbours. This effect would be amplified by the diffusion of such military technology from the steppe"
> Vascon and Etruscan survived (and possibly others)
How about Finno-Ugric? While the Hungarians only arrived about 1000 years ago, the ancestors of the Finns, Sami and related groups have lived in North-East Europe possibly since the last Ice Age (although this is much disputed, and it could be they adopted Proto-Finnic from some later migration).
It depends on how you look at things. The Nordic Bronze age spread around the entire Baltic as well, and genetic markers associated with Finnic cultures appeared much later, and in areas further north and east.
However, as the article mentions, it's unwise to assume there is a 100% correlation between genetic markers and culture/language. The Baltic Sea region has been a trade hub since before the the first indo-european migrations into the area, and some genetic mixing must have been unavoidable.
You’re comment about not assuming a correlation of language and genetics is spot on for this topic. In the linked article (or maybe it was another article on this topic) they mention that genetic research shows that Etruscans shared much of the same step-derived ancestry as the Latin speaking Italians. It appears that, when then step invaders came in, at least one group of them picked up a local non-IE language even while their genetics overcame the original speakers.
This not true. Indo-European diffusion in Europe preceeded Roman influence by at least a half to a full milenium. For example in 500 BC the Celts, the Germans and the Scythians were all speaking indo european tongues while rome was a relatively small republic or kingdom in italy. The italic peoples surrouding the latins all spoke indo european languages except for the etruscans.