Illegal immigration and what happens in other countries are at best a red herring here because illegal immigrants aren't typically eligible for benefits and are typically working off the books. The US government has responsibility for its citizens, not those of Mexico or Latin America.

Also keep in mind many of the proposed redistribution efforts fall squarely in the "equality of opportunity" column which you claim to support. For example, free or very cheap higher education. If we want to be as educated as the Nordic countries this would go a long way. Or taxpayer funded healthcare. This would both reduce the total cost of healthcare and also greatly improve access. It's hard to pull yourself up by your bootstraps when you're sick and can't afford to see a doctor.

Perhaps let me turn this conversation around. Rather than throwing up your hands and saying "it's complex", what specific policies would you support to improve equality of opportunity?