PBMJ = Prescription Benefit Misjudgment.
At the most obvious level, some of the costs of a federal PBM would, inevitably, be hidden in other budgets -- the Social Security budget, the HHS budget, the catch-all budget for government office space, the pro-rated share of interest on the national debt, ad infinitum -- so that there would be a cost bias in favor of the federal PBM, except to the extent that federal agencies systematically operate less efficiently than private firms.
At a more subtle level, since the federal government has powerful incentives to emphasize budget savings over formulary expansion, the mythic federal PBM would attract relatively healthy seniors and/or those who disproportionately use less-expensive medicines and are willing to accept sharp formulary limits in exchange for lower premiums.
Private sector PBMs, because of a standard econometric adverse selection process would, obviously, attract those seniors who anticipate the need for more expensive medicines and, therefore, desire broader formularies; and an increase in the premiums charged by the private PBMs would exacerbate the problem by further concentrating high-cost seniors in the private PBM market.
This is quite apart from the problems created by a subsidy formula based on "average" premiums. The end result would be a market without the private PBMs, that is, monopolized by the mythic federal PBM.
Net/Net: a back-door route toward a VA-type pricing system.
Thanks to economist extraordinare Ben Zycher for the deep dive on PBM-land.