The greatest harm is the numbers - that each wasn’t just sprinkled through and thus left to assimilate but in large enough numbers to congregate, create enclaves, resist assimilation.
Thus you had the Armenian quarter in Jerusalem for centuries, China-towns that have lasted 100-200 years, etc.
Prior to 1965 the vast majority of immigration to America was from Europe. Most immigrants were basically cousins of the original American stock.
The 1965 law dramatically changed the source countries of immigrants to the US, altering the ethnic and racial composition of the country. The new groups don’t easily assimilate and often have no desire to anyway, they wish to retain their old culture and habits and expect Americans to assimilate to their ways.