This happens with (theoretically) non-profit insurers, too. Like the BCBS networks.
Anecdotally though, I've found that my current insurer (United) denies and delays care far, far, more often than when I had a similar plan with BCBS. And I'm not talking about small bills, my son was in the NICU for 41 days, at a cost of ~$150,000. Through BCBS I paid like a grand of that. United denies the most random things, a referral to a specialist, meds for on brand usage while they'll pay for other meds that are off brand, for instance.
I do have a platinum level plan, I am _extremely_ lucky to have this. I know the vast majority of Americans, most of my friends and family, fight with their insurance companies for far less than my complaints.