I'm not asking you to look at anything. Many US healthcare payers are private non-profit corporations. That includes some (but not all) Blue Cross Blue Shield Association licensees. The BCBSA isn't a payer itself and merely provides some shared services to their independent licensees. Outside of the Blues system there are other large non-profit payers such as Kaiser Permanente, HCSC, Geisinger, EmblemHealth, etc. This isn't secret information, you can just go look it up instead of arguing.
Commercial health plans have conflicting financial incentives. Most of them no longer provide much insurance (in terms of bearing financial risk) but rather primarily act as administrators for self-insured employers. So while payers can potentially boost short-term profits by paying out higher claims, employers comparison shop between competing health plans every year. Your HR department would happily switch from Aetna to Cigna (or whatever) next year if their analytics forecast shows that would save a few dollars on expected claims.
Ambulance fees are a mess but those represent a tiny fraction of overall US healthcare spending. Some reform there would be a good idea but that wouldn't do much to reduce costs.
Significant systemic cost reductions will require some mix of lower provider wages, care rationing, and reduced spending on new drug and device development. Countries with more socialized healthcare systems are more financially efficient in some ways but they also just do less stuff: less drug development, longer queues for advanced treatments, underpaid doctors (relative to market wages), care restrictions based on QALYs (or similar metrics). Complaints about payer profits, while perhaps somewhat legitimate in certain cases, are largely a distraction from more fundamental problems. That's just basic math dictated by the cashflows. There are no simple solutions and we're eventually going to have to make hard choices. No one wants to face this reality.