What of the Tengri horse warriors of the 7th to 10th century then ? They swept through an area the size of europe in a few hundred years.
Reaching Eastern Europe. Did they covert Europe and the near east to tengri ? Nope the dumped paganism and all adopted one of the other mainstream religions.
How do you know they didnt do the same thing the first time around dumping there language and religion and mixing in ?
What seems unlikely to your seems obvious to me.
Not a good example. You didn't think of the details of this narrative.
1) The Turkic genetic impact was much, much lower in most of Europe than that of the BA steppe people (steppe Turks were themselves highly mixed and mostly Turkified Scytho-Sarmatians).
2) The disparity of sociocultural levels between themselves and the civilized peoples they encountered was even bigger in the Middle Ages than in the Early BA Age.
3) Where the Turks did change their language (usually because they were just a tiny conqueror elite), they adopted several different languages spoken in each given place, not a common unified language across much of the continent, something unimaginable even in medieval Europe, let alone in Early BA Europe. It'd be a real miracle if all the IE warriors arrived at different parts of the continent and they just happened to find exactly the same PIE language and adopt it uniformly, without leaving traces of their own language (unlike Turks in Eastern Europe, whose languages are still there to be heard) and with a very unlikely linguistic homogeneity all across Europe.
4) The Turks arrived in lands that by the Early Middle Ages were already arguably much more populated developed than Europe in the Chalcolithic/Early BA 3500-4000 years earlier. The population of Europe increased tremendously in the Iron Age.
5) Finally, the Turkic warriors didn't dump their language, most kept speaking Turkic or Magyar in the areas they really settled the most in. They even managed to impose their Asian language onto the native majorities (classic example is Hungarian, but also arguably most of Ukraine and Southern Russia, which were Turkic-speaking until the Slavic expansion some centuries ago, which can also be clearly identified in the genetic record) In other places the Turks' genetic and cultural impact was tiny, so of course they were fully assimilated.
6) Changing one's religion and one's language are totally different matters. The profound influence of pre-IE peoples in the cultural aspects of the steppe-admixed BA and IA populations is very evident, but it does not necessarily mean they changed their language, too. Most Turks, where they really settled in significant numbers, kept their Turkic language regardless of their shifting to Christianity, Islam, Buddhism or whatever.
No, I don't think it's "obvious" at all, and the example of Turks in Eastern Europe reinforces my perceptions. We don't know anything for certain, but if a scenario is most unlikely, especially when we know the circumstances of that expansion (with a much bigger demographic and cultural impact), and we know that even the Turkic expansion, with a lower genetic impact and in much more "competitive" circumstances, left a linguistic and ethnic legacy in Eastern Europe still visible even after the subsequent and huge Slavic expansion, then we maybe shouldn't consider it much.