I think the opposite is correct. One of the biggest drivers of healthcare spending increases is, as you suggest in your opening paragraph, that the people making the decisions about healthcare (the people, with the advice of healthcare providers) are not the same as the ones paying most of the cost (the employers, insurance companies, or government). This skews the cost/benefit aspects of the decisions. (Socialized medicine deals with this in large part via rationing.)
But the bottom line is that people are not willing to accept limits on their healthcare, based on “actuarials and value” or anything else. Insurance companies have attempted to do this exact type of cost/benefit process, and what invariably happens is that they depicted as heartless bastards only out for the bottom line. If these companies do something along the same lines, they won’t be considered attractive employers - to the contrary, they will be depicted as abusive employers, making billions in profits and denying their employees necessary coverage (along with inevitable media stories about so-and-so who was denied coverage for some procedure or other and suffered enormously as a result, and so on).
I’m curious as to what they’re up to (I have a professional interest, as a health care actuary) but my initial thought is skepticism as to whether these companies can accomplish anything that the big insurance companies - with their armies of actuaries, underwriters, and health care experts - can’t do. (It’s very possible that all they’ll end up doing is just creating their own captive insurance company, with perhaps minor differences from other companies - in which case the other insurers can lose market share but the overall market is unaffected.)