Though I understand the possibility (and even likelihood) of an ultimate South Caucasian homeland for the earliest form of PIE, I somehow find it difficult to understand that, in the ancient world, the steppe populations would've been linguistically assimilated by a South Caucasian population even before the Bronze Age (that's if Repin/Yamnaya is already a sign of that acculturation) without any significant or even minor male dominance. Centralized states with an official language can be ruled out for that region as early as that period, and there was certainly no permanent long-distance contact, otherwise we'd expect the 2 regions to have become much more similar in their Y-DNA and Mt-DNA makeup. Would this Indo-Europeanization have happened without any appreciable migration and mostly via maternal lines? I try to accept this scenario, but the details of how that linguistic shift could've happened do not seem to be clearly explained (or even understood as of now).
Maybe more advanced civilization with much more population in the south forced the steppe population to assimilate into them? Steppe population need to know the language to communicate, trade, work etc. with them.