Why don't health insurance companies improve if they are all competing against each other?

I just saw Michael Moore's film "Sicko." What I don't understand is why health insurance companies don't just improve through the normal competition that exists in a freemarket. If the companies are so greedy, why doesn't a new company simply emerge that is a tiny bit less greedy and makes it a little easier on the consumer? Wouldn't that company steal all the customers away and be more successful? Do the insurance companies have monopolies? Is there some reason why antitrust laws don't apply to them?
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One reason is that health insurance is tied to your job, so you as an individual don't have any negotiating power. It's up to your employer to negotiate a group rate. The bigger the employer, unfortunately, the better the rate. That's why small companies either don't offer insurance as a benefit or why they can't cover it 100%. There is just not a lot of incentive for insurance companies to lower prices. The other reason is that Medicare pretty much sets prices for services and all other insurance companies follow suit.
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