Why would rich people leave a comfortable life, to come to the US, then start from scratch?

You're skipping a lot of nuance. The common denominators of your classical Ellis Island "Give me your poor..." steamship immigrant class were

-Very strong work ethic
-Tolerance for risk taking
-Strong religious/familial support structures
-Existing networks to plug into

Rich people are more likely to have become rich as a result of strong life choices made over the course of decades. The vast majority of them aren't born that way. They made it by and large by having those 4 traits.

Take away 1 or 2 of them and what do you have? Somebody who never takes a chance, lacks a strong grounding influence for decision making or just chooses not to work hard. That person *never* becomes rich. Often the exact opposite.

America was built by people who believed - then later proved - that if you work your ass off you'll be rewarded for it. That's the kind of immigrant you want breaking down the United States' door to get here and it's the kind of immigrant we've traditionally been blessed to receive. It's only in the last 8 years or so where the left has somehow decided to forget what actually went on at Ellis Island and pretend that all this time we've just let anyone in for any reason and asked nothing of them. That's not what the history shows.