The doors were never open to Chinese immigrants except for limited periods.
Mass Chinese migration to the US only really began after the Civil War, and was quickly locked down with the Chinese Exclusion Act [0] only a few decades after the doors were "opened". Even then, naturalization of Chinese citizens as US citizens was still restricted. There even had to be a Supreme Court case to establish that the children of Chinese immigrants born in the US were US citizens! [1]
The Chinese Exclusion Act was only repealed in 1943, when a small number (literally hundreds, almost nothing) of Chinese migrants were allowed in, with that increasing slowly over time.
Even today, Chinese and Indian (and others, but the impact is greatest for high population countries) migration is limited by the H1B cap and multi-decade green card queues. If the queue to get a green card is so long that you'll die first [2], you have effectively been banned from permanent residency and naturalization.
My point is simple: doors were open to European migrants, so European migrants built the US and formed its national character. Other methods and types of migration may have also worked to build the US, but we'll never know because the US restricted them heavily and still does.
Chinese laborers, for example, built the western part of the transcontinental railroad. A pretty substantial contribution.
And FDR interned 110,000 Japanese Americans in WW2. My dad who lived in Long Beach at the time said much of this was motivated by envy, as the Japanese Americans ran prosperous farms and businesses.
Practically irrelevant. Brazil and Peru opened their doors to Asian immigrants but just like in the US, they were second wave immigrants and they couldn't save either of those countries.
You need the initial immigrants to do the heavy lifting, plus they majorly control politics.
It's entirely possible that the US would've also succeeded had it opened its doors to millions of East Asian immigrants, but that didn't happen.