First off, for a fun treatment of essentially this exact question, I'd highly recommend the documentary The Search For General Tso, which is focused on that dish in particular but goes through the history of Chinese food in America.

To answer your question, it comes down to a number of factors, one of which was the discrimination that Chinese immigrants faced upon coming the US in the 19th century. There were over 100,000 Chinese immigrants in America by the late 1800s, mainly concentrated in California, and as with many immigrant groups, they experienced racism and discrimination. This led to ethnic enclaves, the "Chinatowns" you see around many cities, where they lived and operated businesses, including restaurants. These were often areas of ill repute, with brothels and opium dens common. This is where the sexualized stereotypes of Asian women first started taking hold in America, and also where the opium-addled Chinaman stereotype came from.

Now, we don't have a ton of brothels and opium dens all over America, but two other businesses also became popular: laundries and restaurants. The restaurants, which started off catering mainly to other Chinese immigrants, adapted to their American surroundings and started attracting others, especially fellow miners and laborers who had worked alongside the Chinese immigrants and were looking for cheap food. Chop suey was one of the first big dishes to come out of this fusion, a mish-mash of ingredients stir-fried and served with a sauce.

So, with restaurants, as with laundries, you had a business that could be started with (relatively) little overhead, could be staffed by a few people (like those in a family), and which provided something that people would readily be willing to buy. With discrimination rampant in the job market, these became very attractive options for Chinese-Americans (because along with fresh immigrants, we've got a lot of second- and third-generation people as well).

Now we add in the Chinese Exclusion Act, first passed in 1882 but made permanent 20 years later. Revisions of the law included a provision that allowed for "merchants" to immigrate, while still excluding most other immigration from China to the US. As the restaurant industry fell under the "merchant" category, a system arose among the Chinese already in America to help bring their families and countrymen over. People pooled their resources to set up restaurants and employed new immigrants as cooks, waiters, and managers. These workers learned the trade, and then left to set up their own restaurants as they gained the experience and legal status to do so.

Thus, we saw a proliferation of Chinese restaurants across the US, as families moved to set up shop in towns that didn't already have one, or where there seemed to be enough business to support multiples. And even as the Chinese Exclusion Act and other discriminatory laws were repealed, these became such a part of the American landscape that they continued to be profitable endeavors for Chinese-Americans.