Two things hinder the provincial negotiation power. One is that it's a minority payer. The other thing is that no does not necessarily mean no, and yes does not necessarily mean yes. When a province actually says yes to a drug, then that's great; it's signed a deal if it's taken up the manufacturer's offer. When a province says no to a drug because the price isn't suitable for Canadian value-for-money expectations, private insurers often still fund the drug. So, in essence, they actually weaken the negotiation power of the pCPA process because, by default, the presumption by private insurers is that they'll cover it.
Now, if you had a system in Canada where you legally bound all insurers to say yes when the government says yes and to say no when the government says no, then you would have a system by which you could probably leverage universal purchasing power. Of course, under that situation, you've basically reduced the private insurers to claims-processing agencies, which they are in some provinces like Alberta and Nova Scotia. Private insurers run the claims-processing function of the public programs, and the government manages what's on formulary and what's not, and what the prices are.
If private insurers want to be claims processors under a universal pharmacare program that's publicly managed, that's great. But the deal is that you have to be all in or all out if you're going to get—