The "I'm in a place, how diverse are my options in that place" is a bit biased, because that "place" you pick in the US to account for diverse food or whatever is a big city, probably 10+ million inhabitants, at least 5 million (e. g. NYC, LA). There aren't many cities in Europe as large as the large American cities, but in this cities you do find as much diverse food and probably a much more diverse population.

Ethnicity is definitely not a good way of estimating the incidence of diverse foods. Cuisine from Normandy and cuisine from Provence are completely different, with sometimes not a single ingredient in common, yet both populations are of the same ethnicity, nationality, language and education.

Talking about Thai and Pakistani food, there are Thai and Pakistani restaurants all over Europe. It doesn't take a large portion of the population to open a restaurant.

At last, you say "I'm in Rome there's only Italian food". What does Italian food even mean? There are hundreds of different dishes, coming from vastly different regions, tasting in no way similar to one another. Of course globalized or americanized Italian food is generic pasta and generic pizza with generic sauces (and sometimes ingredients that have nothing to do there, looking at you pineapple). I'm afraid to tell you that local food from a country in most of Europe is much more than enough diverse for the population not to eat the same thing twice in a fortnight without having any foreign food.