They come here because the weather is better, the cost is lower, and the time to minimum proficiency is much less. All of that equates to way the F cheaper than in Europe or Asia. That is the reason some foreign airlines have contracts with American flight schools.
That does not mean the foreign student continues to fly privately or commercially in the US airspace system after reaching the absolute minimum level of licensing. When that student goes back to the airline that sponsored him he will be trained to the airline standard, for better or worse and much of what they learned in the States is either forgotten or not permitted.
Those foreign students who come here on their own dime do it for the reasons outlined above. If they apply for a flying job at home they are miles ahead since local training is either non existent or prohibitively expensive or military. A lot of those students get jobs with very small “bush” outits in 3rd world jungles where they either get very good at flying or die. The survivors bring great skills to their home airlines that the sponsored kids can only dream about.