The profits of the private insurers aren't the problem. It's their overhead, and the overhead that they impose on physicians & hospitals. Those two things together suck up the majority of private health care dollars.
Consider the hours physicians/nurses must spend on the phone getting preauthorizations and filling out paperwork when requested to justify a bill which happens very frequently. There's also the typical 30% overhead for outsourced billing. That means that when you pay a physician $100, $30 of that goes to the organization the physician pays for billing services. The patchwork of different insurance companies & plans and the incredibly complex requirements they each have are so overwhelming that outsourcing is virtually a requirement.
In contrast, Medicare's overhead is in the single digits, and their billing procedure is much less complicated. I know this is politically impossible, but if we changed nothing about our healthcare system except to move all privately insured people to Medicare and set their premiums to cover expenses, health care spending would instantly drop by around $600 billion. Getting rid of many of the onerous and pointless requirements imposed by Obamacare (EHRs, "meaningful use", PQRI etc) would easily chop another $100 billion.
Oh, and add another $100 billion in savings if Medicare were allowed to negotiate drug prices, and got them to the equivalent of what Canada pays.
That's what, $800 billion now? Pretty easy money if we could only do something about the insurance & pharmaceutical lobbies' stranglehold on Congress. The point is that our medical system is designed to flush money down the toilet, and it does so with sumptuous efficiency.