I don't think he blames the immigrants specifically, so much as illegal immigration as an institution. The only "punishment" that most people want for illegal immigrants who have committed no crimes other than the immigration violation itself is for them to be deported, which really does not seem like a punishment at all -- it's just undoing the criminal act. Like if you stole some money from a bank and then had to give it back, but otherwise did not have to face prosecution.

Because what can an illegal immigrant do? They could in theory just rely on social services and entitlements, but I don't think anyone (including the immigrants themselves, for the most part) really wants that. They want to work, and to make money, and the law makes it very hard to do so legally, so they work illegally.

All the barriers you mention are things that we put in place to "protect" workers, but at the same time create a black market that undercuts those very workers.

As for the employers, sure, they are culprits here, but would you rather have them let the immigrants starve? That also does not seem to serve any social good. As for not paying workman's comp, for example, there is already enough paperwork and bureaucracy involved in hiring a legal worker where there are systems that support and administer those programs. If you wanted to offer a workman's comp lookalike for illegal labor as a social service, then that would multiply the effort and cost by a huge factor.