The French and British Empires were diverse. As for the USSR, it inherited its territories from the Tsarist Empire. It had nothing to do with Stalin's ambitions. They actually lost Finland and Poland after WW1/Russian Revolution.

As for the US, its diversity was a result of a policy. If they had not accepted the Jewish scientists from Germany, we would all be speaking German today.

I agree it is a simplistic explanation. But it isn't a false one. It is one of the many explanations why the US has been a far more successful country. In fact, most empires in their heydey had immigrants from countries around them. These immigrants were traders, scientists, authors, military leaders, etc.