The Medicare schedule is generally low because of the negotiating power of the Federal government so when Anthem (or whoever) says something like "we'll pay Medicare rates" or "we'll pay 120% of the Medicare rate" they're really just cutting payments and increasing patient costs. Nothing more.
In the recent BCBS case, all they were doing was saying "it may take 8 hours for the surgery but we're only going to pay you for 3". They haven't made the surgery cheaper to provide. They just wanted to pay out less.
Also, if we're going to simply do everything based on Medicare, why exactly do we even need private insurers? Just expand Medicare to everyone if the schedules are good, right?