"Collective bargaining" is essentially a strategy for contending with a monopolist by getting your own. There are three major problems with it.

The first is that it doesn't actually get you out of the monopoly. If there is an uncompetitive market and you're required by law (or otherwise compelled) to purchase their services, making the buyer a monopsony still doesn't give them any leverage because they have to contract for the services even if the provider won't lower the price, and the provider knows that.

The second is that the purchasing bureaucracy then becomes a target for capture and has all the wrong incentives to resist it. They control a trillion dollars in purchasing power but it's really about a million providers getting an average of a million dollars each. That's the recipe for doing something inefficient a million times over because every provider wants to get $2M instead of $500k and will lobby for regulations or offer kickbacks or commit fraud to get it, and the public doesn't have the bandwidth to apprehend a million individual cases of things going crooked when each one is only 0.0001% of the total. And meanwhile "a million providers" still doesn't imply there is real competition to get you out of (1), because a radiology lab in Philadelphia isn't a substitute for a neurologist in Denver or vice versa.

The third is that you still don't have any sensible pricing mechanism. Even if you have a monopsony, how do they come up with a price to offer? Dart board? Demanding to look at the supplier's accounts, thereby giving the supplier an incentive to waste money because they're getting cost plus? The only real way to give them the incentive to do it for less if they can is to have alternate suppliers so that they each lose the contract if they don't offer the best price, but not having that was the original problem that "collective bargaining" was supposed to address.

Whereas if you instead focus on sustaining a competitive market then "collective bargaining" is just wasteful overhead, because the competition is already keeping margins thin so there is little more to extract from the supplier and you're only unnecessarily subjecting yourself to a layer of indirection and the principal-agent problem.

The reason a vendor can fleece public services in the first place is, somewhat ironically, the limited access to free public records by independent journalists. I’d reckon we need more freedom of information, more regulatory oversight, and more participation by the public. The cynicism that governments are inherently dishonest and feckless (rather than being designed as-such by the self-interested lobbies pushing this cynicism) is one big reason such corruption has become so prevalent.