The theory behind Medicare Advantage is that it would cost the government less than traditional Medicare because the private insurer would be more efficient. Guess what happened.
Well the only ways to make any sort of insurance pool (whether it's run by the government or a private organization, for or non profit) more efficient is to deny more payouts or aggressively select for a less risky risk-pool. Medicare insures everyone over age 65, so the second option doesn't work. You can't just leave half the elderly uninsured because they're fat and likely to run up $100,000 in knee replacements. So you have to deny more claims.
Insurance is brutally simple. Money in, money out. Trying to make your back office more lean with tech and automation has extremely limited returns, because the back office is such a small portion of the total cost structure. 95-100% of costs in any given insurance operation are claims. So everything to do making things more efficient and reducing costs has to do with reducing claims.
It's not that simple. Something like a quarter of all healthcare procedures aren't justified on an evidence-based medicine basis and do nothing to improve patient outcomes. Higher quality care actually costs less. But there's a huge amount of waste and mismanagement at all levels of the system.
In fact, MA costs the government more per person than does TM. MA may have been lobbied for as a cost saving measure. It is, in fact, a profit center for insurance companies.
The insurers are such behemoths and so largely vertically integrated it is controlling the system instead of improving it.
Notice how there is rarely ever any new competition in the health insurance space to drive down pricing.