Imo the issue with European immigration system is that it isn't welcoming for permanent immigration. So high skilled people go to Europe, earn some money and then go back home because they are never accepted as equal citizens in most wester European countries (both by law, but even more importantly, by culture).
In US on the other hand, immigrants can settle in much more easily and call it their new home, and become full fledged part of the society both by law and culturally. Especially in areas like SV and New York.
When you look at leadership (i.e. C-titles, VPs, Founders) of a lot of tech companies in SV and New York, first and second generation immigrants are vastly over-represented.
EDIT: also guess what is going to happen if immigration becomes harder? the outsourcing companies will get better and do the job cheaper remotely from India, so even more of the tech work will just get outsourced, meaning there will be even less tech jobs in Europe. You really can't stop the inevitable consequences of the global free market, unless you want to go full protectionist. So acquiring and KEEPING skilled labor through immigration is probably a much smarter long term choice compared to protectionist immigration strategies.