But of course there are counter examples and there are probably other factors. London's industrial revolution and the boom of the British empire was driven by trade and a scientific revolution. That started with them cutting loose from the catholic church and limiting the power of royals. The resulting influx of people from all over Europe and later the rest of the world probably helped. Some of the more radical people at the time actually ended up in New England where they helped bootstrap the modern USA.
Japan's industrial revolution started with the royals realizing they needed to catch up and importing a lot of knowledge: https://en.wikipedia.org/wiki/Meiji_era. Japan of course did not keep the foreigners but they did catch up in a hurry by interacting with a lot of them. China is doing an interesting reverse take on this where they send people all over the world and they then bring back knowledge.
So, yes it's not all black and white. But this stuff usually starts with places being open to outside influences and importing and generating a lot of new knowledge and skills locally. Typically, with the help of foreigners in some way. London is a melting pot of nationalities from all over their empire. And the US bootstrapped from the British empire and absorbing bits and pieces from other European colonists (Dutch, French, Spanish, etc.).
The proof was given.
> It's easy to think of counterexamples.
There is a difference between huge cities of cheap labor and innovation hubs.
> you're not exactly seeing a flood of Latin-America-born founders
Maybe not of tech companies, but you'll be shocked how many highly profitable "boring" companies like construction companies, staffing agencies, and auto sales/repair companies are owned by Latina/Latino owners. BTW: owning a business is legal, even if you are in the US illegally, also that has fueled a boom.
Immigration is just a faster method of getting that effect.
Not saying you're wrong.. but what's the proof? It's easy to think of counterexamples. Places like Malaysia that are full of immigrants and are not particularly successful. Or Japan, which is notoriously insular and successful. London has the whole industrial revolution and boom before colonialism and the wave of immigrants
One would also expect a major difference between for instance the US siphoning off the world's top talent (ex: post USSR collapse immigrants from the scientific community) and undereducated economic refugees from Central America. For instance you're not exactly seeing a flood of Latin-America-born founders in the US (not the best metric, but still)