From what I understand, the prevailing academic belief was based on cases where "elite replacement" was what did happen. For example, the Norman conquest of England contributed massively to modern English (all those French load words), and affected the culture in a lot of ways. But for the most part, the actual population movements were smaller. And DNA evidence suggested that several other big cultural and linguistic shifts worked the same way. Mostly the ordinary folk kept doing their thing, while the ruling class suffered upheaval.

The linked article is interesting because it confirms an actual population displacement. Which breaks the recent pattern of studies! But even here later stages were often more cultural shifts than population ones.

We don't know any of this until someone does the DNA studies.