As I see it, the reason Corded Ware and its eastern predecessors are so firmly on the Indo-European horizon is because they contributed a lot of ancestry to present day Europeans. The possibility of Indo-European languages spreading without major gene flow as in the case of Tyrsenian languages is never taken into account for the obvious reasons.
In the latter case there could be no credible attempt to discern between a spread in the Pontic steppe, a naval route across the Black Sea or even the Mediterranean and the West Asian route over the Bosporus.
I deliberately didn't address the issue of the size of the migration when I carefully said:
"I don't know of any reputable scholar who denies that many of the European "Indo-European" languages reached Europe from the steppe along with a migration of people. "
I've been on record for a long time as believing that we have very unreliable data as to population levels in Europe prior to the "arrival" of the "Indo-Europeans". Also, while we have a trail of kurgans leading into Europe from the steppe I've never seen any reliable analysis of how many people from the steppe they might actually represent. It's also important to realize that the trail abruptly stops approximately in the middle of the Hungarian plain. Nor has anyone explained to me how there could have been such massive growth in population levels in the steppe, which the terrain and the subsistence strategies wouldn't warrant, in my opinion. It's only when you get to populations such as Corded Ware, who were not on the steppe, and did practice farming as well as herding that you could get that kind of population growth.
It has seemed to me for a long time that a lot of the movement into Europe was actually of "Indo-Europeanized" forest steppe and forest people, some of them carrying a lot of WHG. That's why I think the "Yamnaya" numbers in certain groups may be inflated, not to mention later population movements that might have inflated such numbers, as in the case of the Finns.
That doesn't change the fact that the Balto-Slavic languages, and perhaps Germanic, can be traced to the steppe, and Celtic and Italic as well.
Whether the "homeland" of proto-Indo-European languages is actually in the Armenian highlands, but then moved to the steppe at least for the "European" languages, leaving the "Anatolian" languages like Hittite behind is another issue entirely. I think that's definitely a possibility, if not a probability. From what I can tell, even the terrain, as well as the flora and fauna, doesn't disqualify it, and we definitely have a movement of the "CHG" component from south to north.
@Moesan,
There is definitely R1b of the right variety in southeastern Europe, i.e. Z2103, which we find in eastern Yamnaya. The problem is that there's very little L11+ and the little that exists can be explained by historical era migrations. That leads to the most vexing problem, which is where were the L11+ people hiding. If we ever get some genomes from the western steppe that might provide us with some answers. Also, once the Balkan farmer paper is published, and if they tested samples up to and including Tripolye, then we'll know if they might have absorbed some R1b there. Or, we may discover that the L11+ people actually took a more northern route.
People who think all of this is settled are mistaken, imo.