There are a lot of rules around how and why you can seek asylum. For one, you have to stop in the first country that is safe to seek asylum, so that would be Mexico because there arent any real wars going on. Also, you cant seek asylum for being poor. It has to be from war or persecution. One can still apply, plead their case but

Really, America's back will break before we could help even a 100th of the world's poverty by just sheer number of people. What's the alternative? Helping them where they live? A lot of the actual problems (corruption in leadership) dont want America's help, nor has American intervention ever really gone well. They have to have a revolution themselves, but how can they when the proletariat can just move to America when shit is bad?