Along similar lines, I read a study nearly twenty years ago and I wish I could find it for these very recurring government vs market debates. The study evaluated prices between single payer countries and found that it wasn’t the collective bargaining that reduced prices in those countries. They observed that there was no correlation between the size of the single payer and pricing. Rather, it was that the pharma adjusted price to minimize counterfeiting and black markets. In countries where black markets and counterfeiting risks were high, the price was lower. Ironically the decision to lower gave some single payers added incentive to participate in arbitrage. One country would be so low the country itself decided they could arbitrage their Higher priced neighbors by selling off their excess through undisclosed side deals. You see a variant of this example playing out between Canada and US. The article talked about individual black markets and state backed black markets that would emerge as a result of these single payer deals... which were supposed to be confidential but of course the black markets allowed pricing information to leak causing everyone to demand lower prices... everywhere except the US which essentially subsidized all of these below market deals that give the appearance that collective bargaining is superior.

Edit: another thought comes to mind - has anyone compared the size of health insurers in the US and compared their purchasing power to government run single payers? I’d hazard a guess that United Health for example probably dwarfs entire single payers of some governments.