I am always confused when Americans use the word 'immigration.' As I was an immigrant to the USA, I am fully aware of the process. All countries require one to complete applications, and they generally work on a points system.
People crossing the border illegally are not immigrants. It's happening all over the world. To all intents and purposes, it is now getting violent. Poland has just given permission to soldiers to shoot people who are trying to cross the border. Europe is turning to the far right because the EU has insisted that people can just arrive (refugees, asylum seekers, etc).
I haven't seen either Obama or Biden stop the border crossings.