Cultural homogeneity I could see. But why would racial homogeneity have anything to do with it?
Today's civic nationalism experiment rejects this link, yet no society has sustained high-trust diversity without such enforced unity. Rome threw everything at assimilation: shared language, values, identity above tribe, and state religion. It still fragmented.
So Western nations face an unprecedented gamble: Can they maintain cohesion without these historical levers? History offers no successful precedents, only warnings.
Two to three centuries is nothing to sneeze at, either. What are you comparing to?