The reality is many people come on temporary visas, as tourists, as students, etc., and overstay. This policy is some attempt to address flows of quasi-legal immigration.
It's unfortunate there's friction to the process, but it's by design. 15% of American citizens and permanent residents are foreign born, the highest it's been in 50+ years, so people are successfully making it through the process. Ideally we'd have better levers to (1) modulate the rate of immigration, (2) simplify the process of legal immigration, and (3) still somehow limiting illegal immigration, quasi-legal immigration, overstays, etc. This is not the ideal solution.
> it feels necessary to say: people who come here to contribute their skills and experience don't all come along on an H1-B/L1
Do people migrate to "contribute their skills" to a foreign country, or to improve their lives? Maybe I'm a cynic, but I suspect the vast majority of people throughout history have migrated to improve their lives, not to altruistically benefit a foreign country. And that's fine, that's normal. It's what motivates people, and the U.S. has a long history of being shaped by ambitious people, especially immigrants, who wanted to improve their lot in life.
> nor do they only come from white or european countries.
I don't know if that's necessary to be said, because who thinks that? In recent decades, 85%-90% of immigrants to the U.S. are not white. >90% if you include undocumented immigrants. The trajectory of America from a white majority to white minority country is fueling at least some of the immigration backlash today. But I think for most people, it's a feeling (right or wrong) that jobs becoming harder to find, houses are becoming harder to afford, and more and more people are competing for fewer resources.