The immigration crisis of today is the result of a failure of legislative body to legislate (10% approval ratings are bad). Including other external factors such as corrupt governments/drug cartels and internal factors such as many companies happy to look the other way when people don't have legal work status.
If you watch videos on immigration seeing ICE, courts, and migrants interacting, the migrants get asylum and then encouraged to find work. It's all tongue-in-cheek. If anything the system could be intentional because without legislation, the executive branch can unilaterally set thresholds and targets for migration in step with economic goals. Even Trump didn't tighten the migration laws drastically until covid hit bringing an economic slowdown (no workers needed during recessions).
The social issues focused on in the media are minor compared to the economic benefits.