This is backwards logic. Those few large corporations have the bargaining power to negotiate lower premiums. Individual consumers have zero bargaining power.
On the other hand individual consumers have ALL the bargaining power - they can simply pick a different insurance company, and insurance companies have to work very very very hard to get customers. They would compete on price because that's by far the most important thing to a consumer.
A company on the other hand cares about other stuff, how integrated in the system, how easy can we import members, manage members, how much marketing material do they give? Do we have to educate our employees, or will the insurance company do that for us?
Just tons of other stuff that isn't price. Individuals: It's 99% price.