The dream is certainly to have a better life. But the reason why qualifications are arbitrary is that about half of those coming and stay illegally are not extremely poor, illiterate people. They have enough money to pay for an airplane ticket and a tourist visa (both of which seem cheap to the average American, but are a steep price in third world countries), passed a Dept of State background check, so we’re not talking exactly bottom of the barrel here.
Then they come here and realize they need to start from the bottom, washing dishes, flipping burgers, and head back (unless they already have family that can put them in a better situation). So there’s a varied demographic here, despite the rapists and felons rhetoric.
EVerify exists and is implemented, the main reason it’s not widely enforced comes down strictly also to economics. Things like farm jobs are already under huge pressure on competivity (tariffs didn’t help that), to the point the government has to subsidize them (sometimes to hire these illegals).
Unfortunately Washington and Business doesn’t want to have an honest conversation about this, and thus neither do we. That is the true immigration problem in this country, and if the power brokers are not interested in a fix, then there won’t be one.