We do not. One of the reason is that we dont have that much Craniometrics datas compared to ancestral components datas for exemple. We do not need facial reconstructions of individuals to know if people are brachycephalic or meso, dolicho. We need intact craniums. The reason to link it with ANE, is because it's the only real ancestral component that links East Asia and West Asia in prehistoric human migrations. All modern people with high % of brachycephalic individuals ( Siberians, Turks-Mongols, East Asians, Southeast Asians, Native Americans, so basically roughly Mongoloids ) are a rumble of East Asian and ANE ancestry with minor other ancestries and the places that we know in western eurasia ANE ancestry irradiated in ( Eastern Europe, Iran, Caucasus ), also shows high levels of brachycephalic individuals and probably irradiated in peripheric areas such as Northern, Central, Western Europe for Eastern Europe. Southeast Europe, Anatolia, Armenia, roughly Middle-East for Caucasus. And roughly Middle-East and India for Iran. There could have been different migrations bringing Brachycephaly in places it wasn't common. Exemple: In Late Paleolithic, ANE individuals could have bring Brachycephaly in Eastern Europe without being fixed in a whole population ( meaning some people were still dolicocephalic and mesocephalic, while others were brachycephalic ). But we also know that Eastern Europe suffered a second wave of ANE ancestry, called WSHG ( western siberian hunter gatherers ) and an ancestry more leaning towards East Asian ancestry labeled Baikal_Neolithic sometimes near the transition between Neolithic and Chalcolithic. So with huge craniometric datas from Mesolithic Eastern Europe ( Ukraine_HG's, Baltic_HG's, Balkans_HG's ) we could already deduce if the physical characteristic came from the 1st or the 2nd ANE wave. But more, Eastern Europe also could had a 3rd ANE/East Asian introgression in the Scythian era, were Scythians were highly mobile in the Western and Central-Eastern Eurasian Plain and could have bring this ancestry in Eastern Europe, and from there the Thraco-Cimmerian migration from the Danubian Plain to Central Europe too. Also the more documented 4th and 5th introgression wich were the Huns ( or early Turkish people in general ) and the Mongols. Plus between the 2nd ( or maybe with the 2nd itself ) and the 3rd introgression, there was a migration of Siberians people that would have bring the Uralic languages at some point wich would also bring ANE/East Asian ancestry to Europe. It makes a lot of East Asian ancestry introgression into Europe right? Now anatomy is not always linked with ancestry movements, but it still can give us a clue.
I think it was James Mallory who said in one of his books that the Dnieper Rapids in Ukraine was in the Mesolithic the warzone between 3 peoples, 1 dolicocephalic and 2 brachycephalic. But i dont know at all if this is backed up by craniometrical facts.