I'm under the impression that there was widespread democide during and after the Norman Conquest, particularly with the goal of eliminating the anglo-saxon nobility and aristocracy.
That is true, particularly in England. However the aristocracy mostly fled to other parts of Britain and Scandinavia; the Saxons certainly remained in force in the labor class and in the genetic pool. Of course, this is less true in England than Wales, Ireland, and Scotland, but saxony was not forgotten, English remained Germanic, and it would take many centuries until the Norman linguistic influence trickled down to the general populace. To this day you sound upper class if you stick to French (Latinate) derived vocabulary.
My point being: the pre Dorian culture remained in Greece as well. The Mycenaeac influence was still visible in the literature of the day as a distinct culture; there was no clear attempt to impose a foreign culture by violence or other aggressive means. Or at least no evidence. Of course, we might know more if we ever get Linear B, but who knows if we ever will.
This is all a very long winded way of saying "invasion" doesn't ever really capture the subtleties of cultural diffusion. Ghengis conquered much of the Middle East, but the resulting cultural change was both more visible in places Ghengis never saw such as Western Europe and it was driven more by trade than by direct imposition.
"Ventris was able to show, ever more clearly over the months that ensued, that the language behind the script was Greek – in his own words “a difficult and archaic Greek, but Greek nevertheless”."
