Your understanding of LLCs is a bit off. The LLC (or other corporate) structure does not protect the nurse from liability, nor any of the other directly-involved workers. The LLC protects the owners of the LLC - ie the ones turning the screws that spread workers ever-more thin. Workers generally avoid being sued mostly by custom, following procedures set by the LLC and/or professional bodies, being "judgement proof" (ie not having significant assets), and various types of insurances.

("Replace AI with 'company' and you realize that we're living in that world already." I 100% agree with this, though!)