They might have played some minimal role, but absolutely nothing significant, at least i am not convinced, sorry.
The Thraco-Cimmerian horizon was culturally influential for generations and connected the Carpathian sphere with the more Upper Danubian and North Italian even more directly than Urnfield before, which was more split into provinces/groups. That's why its important to mention, they pushed and pulled Daco-Thracian elements, which were still concentrated along the Carpathians largely, West and South, both directly and indirectly. Like in the Veneti, Fr?g, Kalenderberg group in Eastern Hallstatt, they all preserved elements of this Thraco-Cimmerian horizon and being directly connected to Basarabi the same time. The network which came up with the Thraco-Cimmerian horizon persisted. The innovations brought by the Cimmerians were spread by the Daco-Thracians, especially Basarabi, too.
We have discussed before, i am of the opinion, in fact, it's very straightforward. Gava/Channeled-Ware along with some other Middle Danube Urnfield, Grla-Mare/Dubovac-Zuto Brdo/Brnjica, Vatin, Paracin/Mediana, Psenicevo-Babadag. All of these had E-V13, some more some less.
Probably, but I think G?va/Channelled Ware is the real core and much of the others being derivatives or predecessors anyway. However, Middle Danubian Urnfield in the narrower sense is probably a group apart, because like I said, they are too much Western Bell Beaker derived, unlike Kyjatice-G?va. I largely agree with you anyway, but Thraco-Cimmerian horizon and Hallstatt is not who got it first, but about who spread it West. Actually its these two cultural formations which brought the Daco-Thracian E-V13 West like a Wedge, right through the more Pannonian-Illyrian Middle Danubian and Para-Celtic territory.
On a large map, you can really see that the Cimmerian and Scythian intrusions into the Carpathians pushed many elements, almost all Daco-Thracian in origin, West, first while fleeing from them, then with them, later by people which copied 1:1 Cimmerian and Scythian styles, but being genetically fully Daco-Thracian and Pannonian. Whether they were E-V13 dominated or not, autosomally that's clear.
I find the Thraco-Cimmerian label ambigious, we don't know who they were, and where did they come from, what language did they spoke, and who were their descendants. It's all open to interpretations.
We have some "original Cimmerians" and they are pretty mixed. Like one in Central Europe had haplogroup N and was autosomally quite different from the Kyjatice sample BR2, I wrote about it here:
https://www.eupedia.com/forum/threa...kan-case/page8?p=633773&viewfull=1#post633773
So you see two completely different populations, one being related to Vatya, Mako, Epi-Corded and the other wild mixture from the East. The first are Daco-Thracian related, Pannonian-Carpathian Urnfielders, the second the steppe alliance of the Cimmerians.
The point is, they introduced and spread iron working techniques, they did introduce new horse gear and tactics, most likely new horse breeds also. And these spread among the elites of all Eastern and Central European groups, throughout most of the Urnfield networks, but not all. Like the Transcarpathian G?va people resisted in fortified areas for a prolonged period of time and got less Thraco-Cimmerian horizon influences than Basarabi!
But otherwise, you see the whole elite from Southern Germany, Northern Italy, Austria, Hungary, Croatia etc., they all adopted the whole package or many elements of it. And those which adopted the most from the Thraco-Cimmerian horizon and kept these traits the longest are the groups closer connected to Basarabi too! Like Fr?g and Kalenderberg for example, vs. the much less influenced Unterkrainische group, which was more in the Illyrian tradition.
There you see that after the initial impact, Thracian and Cimmerian elements fused to something new, which was fundamental for the final stage of the Bronze Age and the introduction of Hallstatt. But Hallstatt was full of elements from Channelled Ware and Encrusted Ware influences too! That means you see here two main elements at work: Thraco-Cimmerian horizon/Cimmerian influences, Channelled Ware traditions with Encrusted Ware influences.
"Hallstattisation" is basically Channelled Ware with Cimmerian ideological-religious and material influences from my point of view. That's what really brought it West. Because where G?va Urnfield stopped in Eastern Germany, Bohemia, Austria-West Hungary etc., Hallstatt went right through and Thraco-Cimmerian elites with it.
We know it from the "Scythian" finds too: In some there were mostly or even pure Daco-Thracian and Pannonian people, but sometimes in complete "Scythian gear". That's just what the elite warriors adopted and the lifestyle the surviving locals embraced. The question is how much paternal replacement the Cimmerians and Scythians caused, but in my opinion not too much, because the haplogroups associated and found so far were much less common afterwards than the rather Thraco-Illyrian ones.
Like Yamnaya thousands of years before: The initial impact was huge, but the genetic legacy comparatively small. Same for Cimmerians and Scythians, but apparently not the Daco-Thracians which spread the fused culture, they had more of an impact. For the Cimmerians we don't have enough samples, and the rite of cremation among many of the Channelled Ware and Eastern Hallstatt people makes it difficult, but for the Scythian case some generations later, its easy to see:
https://ibb.co/cCKD3Bj
There are relatively "pure", "mixed" and "local" individuals within the "Scythian" cultural context. There was also exchange between the Pannonian Thraco-Scythians and the Moldovan Geto-Scythians. There are outliers in the clusters of the respective other group.
Thraco-Cimmerian elements in the burials, which is the main thing, will be even more "local" or in many Eastern Hallstatt instances Daco-Thracian/Basarabi related than these. The elites in Fr?g buried as horse warriors are likely to have been very strongly Daco-Thracian/Basarabi influenced. Unfortunately they mostly cremated, but we know from the inventory that both male and female elite individuals moved from Basarabi to Fr?g, but there is little evidence for a movement in the opposite direction! So the whole Thraco-Cimmerian horizon and Hallstatt based on it created a primary mode of cultural transmission and people moving from East (Carpathians and further) to the West (Danubian-Alpine sphere). That's true for the formative period of early Hallstatt in particular.
Pre-Scythian Mez?cs?t = Thraco-Cimmerian core. It shows primarily steppe Cimmerian elements on top of local Channelled Ware people. Like I said, the tested individual was East Asian admixed and had yDNA N. Let's see what others might bring. Probably some being in the new British paper, because they didn't cremate...