They do indeed have established processes. And the US violates the shit out of them and illegally detains people against international law. You really think the UN established processes involve caging people without checking their credentials or asylum claims? Do you think international law is big on freeing up border guards to violate civil liberties of both citizens and immigrants? No. After the Holocaust, where many countries turned away fleeing Jews, who would then end up getting gassed, the US made sure the UN implemented international law that would make seeking asylum more human rights friendly.

Then we started violating those processes and cracking down on immigration, which actually increased illegal overstays because people stopped going home after their short term visa jobs because they knew they couldn't come back next year to pick strawberries if they left. This isn't wokeism, it's just history.