This is a very very unlikely scenario considering the very little time gap between the proposed dispersal of Steppe Indo Europeans and the age of these Hittite Bronze Age samples. if these Hittites really came from a roughly ~40-50% EHG source. You would need at least a century until the EHG get's deluded down to 6,25% per individual. And this is only possible if you assume the "Hittites" exclusively and rapidly mated only with individuals with zero EHG. That even excludes other EHG mixed Hittites. How often do you see it happen that people of the same folk do not even touch each other over the course of 4 generation? Even in societies with high mixing rate you always see more a pattern like this.
1. gen
same + foreign, same + same, same+ same, same+ same
2. gen
1/2 mixed + same, same+ same, same+ same, same + same, same + foreign
3. 1/4 mixed + same, same+ foreign, same+ same, same+ same, same+ same, same + 1/2 mixed
And this is rather the pattern for a mixing society.
And in this scenario allot of the foreign admixture actually get's washed out. And the mixing on basis of DNA is much slower. "Steppe" Hittite with 40% EHG mixes with 1/2 mixed "~20% " EHG result is =30% EHG. That 30% EHG mixes with a "full blooded" Hittite result is 35% EHG. This 35% EHG Hittite mixes with a 20-30% EHG Hittite result is 27,5% to 32,5% EHG. Keep in mind and this is the pattern for a strongly mixing society because it is never linear.
But for your theory above to work you would need to assume something more like this.
1. gen
same+ foreign, same+ foreign, same+ foreign, same+ same
2. gen
1/2 + mixed, mixed+ 1/2 mixed, mixed+1/2 mixed, mixed+ 1/2 mixed
As if they were always exclusively mating with foreigners and killing of those pure "Steppe kids".
So no I don't agree with this. There must be a different reason why BA Hittite samples lack EHG just like the Calcolthic Hajji Firuz sample a little further east. And both being basically a mix of Iran_Neo/CHG and ANF.
I think the authors are holding back something.
Well, I don't there is a "little time gap" between the split of Proto-Anatolian and the first absolutely confirmed Hittite presence in Anatolia around 1700 BC. According to linguistic evidences, Proto-Anatolian may have set apart from the other Indo-European communities as early as circa 4000 BC. Nobody (not linguists and most geneticists, anyway) assumes that the Proto-Anatolian dispersal happened along with the early-mid BA dispersals of other "late PIE" branches from the steppe. Some of the latest estimates still date that split to around 3500 BC, still virtually 90 generations before the first undeniable Hittite prevalence in Central Anatolia. With that very early split, there was enough time for us to assume several plausible different possibilities - and we'll need more data to settle what's really likely or not.
A lot of different processes of Indo-Europeanization, including a complete revolution in a people's autosomal makeup, could happen in ~2300 years, especially if the Hittite society was, as it seems from archaeological and linguistic evidences, mainly a result of a gradual, non-massive infiltration and/or eventual elite conquest. Just look at some Turkic-speaking populations now and how much Northeast Siberian and East Asian they still carry after a mere ~1500 years of immigration, mixing and acculturation.
My scenario for the progressive and profound regression of the EHG does allow for a lot of Hittite-Hittite relations, actually my "hypothesis" allows for a significant, even though minor, autosomal contribution from a EHG/CHG Proto-Anatolian population (which of course means that a large part of the offspring involved relations between two peopel of full or major PIE ancestry).
You're thinking of 3 or 4 generations, but when you consider that there was very probably at least 50-80 generations between the Anatolian vs. Residual PIE divergence and the Hittite kingdom/empire, that possibility becomes much higher. That autosomal transformation can happen in the long term even in the absence of any complete population replacement. It's simple to demonstrate, doing the maths, how that could've easily occurred given the historic conditions for that. In a hypothetical and evidently simplified scenario (the same thing, only with much more ANF than EEF, would happen in a Balkanic route):
1) Pre-Proto-Anatolian PIE-speaking population: 40% EHG. 60% CHG.
2) Proto-Anatolian population (mixing with Caucasians with little EHG, ~5%, but ~70% CHG and ~25% ANF), contributing to an appreciable 30% of the future population >>>> 15.5% EHG, 67% CHG, 17.5% ANF.
3) That Pre-Hittite Anatolian IE population heading to Anatolia, absorbing conquered and allied people (virtually 0% EHG, and assuming some 30% CHG, 70% ANF), and mixing more along the way, contributing to a large 45% of the future population: 7% EHG, 47% CHG, 46% ANF.
4) Early Hittite population in Central Anatolia, infiltrating gradually, slowly gaining prominence, and mixing with the local, presumably very large and advanced population of Hattians and other farmer people (still contributing to a sizeable 20% of the local ancestry of their future empire): 1.4% EHG, 33.4% CHG, 65.2% ANF. - Of course just an average, so if the average were 1.4% a lot of people would have 0% EHG (and we have very few Hittite or "Hittite" samples), but some others, probably a small minority, could have 10% or even more.
I don't really support this scenario more than any other, I'm just trying to think of all the possibilities that are still rightly on the table and haven't been completely debunked at all - and I think people shouldn't believe that those few supposedly Hittite samples settled this once and for all, no geneticist has affirmed that).
I myself believe that it is probable that PIE originally came from the South Caucasus, and those origins are probably showing in the large increase in CHG ancestry that even the Eneolithic Steppe by 4300 BC already had, and the fact the authors of this paper apparently differentiate between the CHG in Caucasus populations and the "CHG-like basal lineage" in the steppes.
However, for me that's an entirely different thing from stating that the PIE expansion came from the South Caucasus. Those are not just two different issues, they also most definitely happened at different times and under different historic contexts, because PIE is simply not that ancient and there was probably a wide time gap between the gradual splits of its IE daughter branches, beginning with Anatolian probably more than 1000 years before, say, Indo-Iranian. If IE came to the steppes with CHG people, but that happened during the early Neolithic, then Proto-Indo-European (the latest stage before the formation of several IE branches) may be just the daughter language of that ancient CHG language, and not the same language (and also not the same people). Since no study seriously doubts that at least several branches of IE are connected to the BA steppe populations, then the real question is: did IE develop in the steppes very early on in a still undivided form, or is the "steppe IE" the very result of the 1st divisions of PIE?
If this study really suggests, as it seems now, that by 4000 BC the steppe population's autosomal, Y-DNA and Mt-DNA makeup were all basically consolidated and not significantly different from what we'd see later with the expansion of the Yamnaya horizon, then the origins of PIE - whether it was originally EHG or CHG (coming from Transcaucasia) - are further back in time, and it was not brought to the steppes at roughly the same time as Proto-Anatolian IE diverged from the rest (that assumption of a two routes dispersal: one forming Anatolian, the other forming the direct ancestor of "the rest" i.e. Late PIE). The origins of PIE in the steppe would be more ancient, and no big Caucasian influx happened in the transition from the Chalcolithic to the Bronze Age (so who would've made the steppes speak PIE? I really doubt people just adopted the language a distant foreign people with whom they have few contacts in times before centralized and civilized states).
As I said, I think there are now many more questions and possibilities than answers. I don't really get why some people are becoming so confident to affirm either this or that hypothesis of their liking.