No, actually this is the benefit of collective bargaining. When you have a single entity that represents millions of customers, you can say "we'll take this, but only if you drop the price by half and not raise it for ten years" versus an insurance company that is not only incentivized to take a cut, but often only represents thousands, with the biggest that represents hundreds of thousands being able to point at the little guys and say "we're still cheaper than them" even if they still charge a hundred dollars a month for insulin.

This is one of the advantages of public healthcare, and why it's so important we preserve it. Hell, it benefits those that go to private hospitals as well, as everybody benefits from the lower drug prices, not just those who go to public hospitals. Well, except those that sell the drugs, but that's why so many conservative leaders try to cut public healthcare, because they're in bed with somebody in the distribution chain, and even if they're not, they're easy to bait into taking such measures.