Administrative fees include profit, but also salaries, IT expenses, whatever other costs it takes to actually run an insurer.
That is to say, there is an incentive for higher overall insurance spend, because it allows for higher admin fees (including profit)
State insurance laws have mandated the same kind of caps for decades... I believe they date back to around WWII, but I don't know for certain.
Every US state has laws that prohibit insurance companies from collecting "too much" profit from the premiums they charge their customers. In most states, the limit is given as a percentage of pure profit. So insurers set their premiums based on their expected payout costs plus operating expenses, and usually make premium adjustments on an annual basis.
(That's why most US drivers received a bunch of rebates from our auto insurers, early in the COVID pandemic. The sudden unexpected drop in accident rates drastically reduced the insurers payout costs. They were required by law to return the excess.)
The intended purpose of these laws was to protect consumers from predatory insurance companies. But in modern practice, with basically zero effective cost controls on medicine, it's created a perverse incentive: Rising healthcare costs are the easiest opportunity for health insurers to increase their absolute profits... All they have to do is sit back and let health care providers keep raising their prices.
But:
• the costs are passed only indirectly to the consumers who ultimately pay
• the market for health care is so terribly distorted
• health care demand is highly inelastic
So normal market mechanisms (like price signaling) aren't very effective at containing the rise in costs.
Further, most bigger companies self-insure, and only use the insurance company to provide services. So F100 company partners with Blue Cross Blue Shield just for billing, administration of the plan, etc. What does BCBS care how much surgery costs? They are getting Admin fees the same whether its $5,00 or $10,000. Does a F100 employer really have the time and energy to question whats going on? They just look at the cost last year, raise the price for their employees by %XY and march forward.
Even further, health insurance is incredibly regulated, on a state level. If you have a good idea to "disrupt" the industry, its such a slog to get anything done. Your best bet is to partner with an existing insurance company and go from there.
But the managed care organizations (health insurance companies) still complete with each other. UHC, Anthem, Cigna, CVS, Humana, Centene, etc. there are many.
Considering they all have low single digit profit margins per their 10-K reports, it seems evident that there is sufficient competition to incentivize low prices for managed care services.