I can offer a partial answer offhand but without citations, so if that violates the sub's rules then mods please remove. This is more of an /r/askacook level response so it may not be allowed here.

The two biggest factors in the answer to your question are the technology of food preservation and the development of the idea of nationalism. An obvious third is the technology of transportation, but for my purpose I'll assume that preservation & transportation go hand in hand.

Preservation techniques logically innovated ahead of ideas of nationalism and "national cuisines." Grains have been and still are the universal human staple where easy preservation (like refrigeration) isn't available. Preservation techniques also relied on farming seasonal crops as efficiently as possible so that people didn't have to spend every waking hour in search of food. If a thing was out of season where you lived, it was probably unavailable as an ingredient. In preindustrial cultures fresh meat is terribly expensive and is therefore a prestigious delicacy typically reserved for the elite or for special occasions. Other meats are traditionally preserved using non-refrigerated methods, such as curing with smoke and salt, or brining with oils and vinegar, or by fermentation. While these methods have yielded some of my favorite foods, their taste follows their function and they're generally extremely . . . savory, which puts constraints on their application. So while there are many Sicilian dishes that use fresh anchovies, if they were transported any distance as, say, a ship's rations, they would have been salted and brined into the small brown thing most of us are used to declining on our pizza.

The science of food preservation didn't really advance past this from the agricultural revolution to the 19th century. One of the reasons that Chicago became an economic center in the US was the invention of the refrigerated train car in the mid-1800s and the overshadowing of water transportation by rail transportation. Refrigerated train cars suddenly allowed meat that was farmed in the western states to be transported freshly to the east, changing the dietary landscape of the entire country.

So the seasonal relationship with diet, the scarcity of non-local ingredients that could only be transported using a limited assortment of preservation techniques, and the absence of the economy of scale that makes meat cheap and widespread today all meant that a Roman living in what is modern-day Turkey might have some exposure to preserved foodstuffs and wines from Egypt, but wouldn't have a food-court style concept of "Egyptian" food.

They also wouldn't really have a concept of "Egypt" as a centralized place on a map with impermeable borders containing a specific palette of foods. Nationalism was another 19th century innovation, like the refrigerator car, that sped unifying trends through Western culture. What I think of as Italian or German food can obviously be traced to pre-Roman roots, but neither were solidified as single nations until the mid 1800s. Similarly the British Raj had an exchange with "Indian" food that can be felt today, but their colonial governance shaped what would even be thought of as "India" for reference by outsiders. Milan, Bavaria and Kashmir all have regional dishes, but a 19th century Londoner wouldn't have thought of a restaurant that served a Kashmiri-inspired dish as being something outside of the experience of "English" food, i.e. "You know what? Tonight I want Indian food."

The UK's famous relationship with curries was introduced in the 1930s and popularized in the 60s-70s as the Anglo-Indian hybrid we know today. Probably the longest-standing relationship with "ethnic" foods in the United States - and here it's important to remember that racism and segregation plays a big part in the answer to your question - is with our Chinese communities, who were regarded as so "foreign" that the safe enclave of a "Chinatown" is such a truism in most large US cities that they're celebrated historically. But they originated as ghettos and safe havens due to the racism with which Chinese immigrants were met in the US in the 1800s as they arrived seeking work and opportunity. These enclaves soon had sophisticated restaurants that served a mostly-Chinese customer base, and elsewhere Chinese restaurants provided employment for workers who were shut out of opportunities elsewhere due in part to their ethnicity. By the 1920s restaurants serving Americanized interpretations of "chop suey" had become popularized. In the 1970s the US was introduced to expanded Asian cuisines due to immigration of Southeast Asians, and this is where the current idea of "fusion" cuisine has its origins. Sushi began to be popularized in the US in the 1950s.

Following WWII, the United States and Europe had a post-colonial diversity of global immigrants like never before, a strong sense of national identity (to distinguish one's "own" food from that of others) solidified by two major conflicts, and the technology, infrastructure and economy to support the relatively new idea of everyday eating as pleasure. A watershed for US cooking was the 1961 publication of Julia Child's most famous book, which introduced the principles of "French" cooking to American kitchens in a historically unprecedented climate of ideas - the postwar prosperity culture was well-travelled due to two World Wars, was vertically aspirational with wealth to match and, despite the pervasive racism that still exists today, held a more cosmopolitan perspective on the purpose and pleasure of eating than their medieval counterparts did. In the centuries leading up to the Renaissance, a meal was thought of as having components that complemented the body's humours and was valued for not being rotten. In the 1960s, social, scientific and economic advancements meant that a meal could just be Japanese.

edit: added two suggestions for further reading and re-qualified my answer in the first para.

Two outstanding perspectives on your question are provided by the books "Near A Thousand Tables" and "The Pig and the Skyscraper." TPATS is a social history of Chicago, but its scope includes such a restructuring of the way that Americans conceptualize food that OP might enjoy it.

Can I piggyback a similar question off of this?

When did "going out to eat" become a thing? If ancient Romans decided to have Egyptian, did that come after debating eating at home? Or was there a period where people didn't eat at home, or vice versa?

Cookbooks have been around for a very long time. Mithaecus, in the 5th century BC, brought Sicilian cuisine to Greece partly by writing cookbooks. These recipes could be very vague, however, with simple directions like "cook with cheese and oil" without specifying what type of cheese, or how the cheese should be added, or how long to cook for. As a result, foreign chefs were in some demand. There are stories of particularly rich or powerful Greeks and Romans seeking out chefs of a certain nationality simply because they wanted to eat certain dishes.