What is being ignored, AGAIN, despite all the papers and all the threads and the reams of posts is that there isn't a one size fits all "invasion".
What went on in parts of the northern border regions (and perhaps even Britain) that were barely populated was different from what went on in a Central Europe that had experienced population crashes and was perhaps weakened by malnutrition and the diseases (the plague) perhaps carried by the new arrivals, which was different again from what happened, perhaps, in southern Europe, or in Anatolia and Iran, etc. in the Near East.
There are also big differences by time period. I know some people in this hobby, particularly young men, love a sort of Conan the Barbarian or Viking kind of narrative, but it doesn't fit a lot of what went on. Corded Ware only got a little bronze at the very end. They barely had copper weapons. They did not have a big military superiority over the MN people they encountered. That's very different from the Mycenaeans, for example.
You can't make one story fit all.
What I do think is true as a rather global matter is that you often have a civilized "core" built up over generations and hundreds of years which starts to develop problems, perhaps because of climate change, or environmental damage, or class differences which result in mass conflict, and populations of the periphery, perhaps nomadic herders in some areas, swoop in and take over, sometimes with pretty significant genetic changes altogether, sometimes as an elite, sometimes with broad autosomal replacement, sometimes with autosomal admixture but a yDna sweep. You see it in China, in Africa, in the Near East. It has nothing to do with "superiority" whatever the racist "philosophers" and anthropologists of the late 19th century might have thought.
If you have never read or have forgotten about all of this, you can find detailed discussions about these matters if you use the search engine.