While it's true that a cartel would be the fastest way to raise prices, I don't think that not having one removes all incentive to try.
I think you're also ignoring healthcare networks. This is important for two reasons.
1. The kind of supply and demand works very well for modeling commodities, but the difference in networks means it's very hard to have two completely equivalent insurance products.
2. Insurance companies can incentivize hospitals to behave in certain ways by regularly pruning those who do not behave that way.
Also, most people get their healthcare from their employer. There's not as much ability to actually switch, unless you're so fed up that you're willing to switch jobs.
I think you're also ignoring healthcare networks. This is important for two reasons.
1. The kind of supply and demand works very well for modeling commodities, but the difference in networks means it's very hard to have two completely equivalent insurance products.
2. Insurance companies can incentivize hospitals to behave in certain ways by regularly pruning those who do not behave that way.
Also, most people get their healthcare from their employer. There's not as much ability to actually switch, unless you're so fed up that you're willing to switch jobs.