There are certainly a lot of diaries, and discussions, on KOS about the evils of for profit insurance. In addition, to the actual profits there is the issue of executive compensation, which is common with other large corporations. Many people feel that if it weren't for this money being bled out of the system, people would be better covered for less and thus even more people would sign up for insurance. This is one of the driving forces behind the public option. However, if this is all true, there is a simple way to demonstrate it:
Start a non-profit health insurance company.
I have to admit, that I don't really believe that the profits and executive compensation are the source of the problem. I think that actual health care costs are the real problem and that changing the way we insure people will not solve it. However, if I am wrong, then someone or some group of people could start such a company, make a good, but not excessive (avoid excessive compensation), living doing so -- as well as making life better for millions of people. Certainly worth doing, if you believe that insurance company profit is the source of the problem.
It's not so impossible to start a company, or a non-profit organization. In California, it costs a few hundred dollars. Of course with something as important as an insurance company, you need legal advice, but there are lots of lawyers who could probably help a good venture.
The biggest problem I see is that of getting some assets. I'm not an insurance specialist, but I strongly suspect that regulatory agencies are not going to let you start selling insurance unless you have deep enough pockets to pay reasonable costs. Since you wish to be non-profit, you will not be able to get investors in the traditional sense, as you will not be able to offer them profits as an incentive, but you may well be able to find some people of means to donate, or just have a lot of small donations.
Limit your salaries. The CEO gets no more than $300,000 (that's half what the CEO of the Red Cross gets), and that only after you have revenue exceeding a billion. There certainly is enough room to make a decent living without having to get into 7 figure salaries. The extra money can go to pay claims -- or lower premiums.
Initially, you would probably have to purchase a policy from some other insurer to cover you in case one of your first policyholders gets unlucky and racks up a 7 digit expense, but that shouldn't be too expensive because it would probably be a $500,000 deductible or something like that.
You can set the rules, make it your business to keep care high and premiums down. If the economics work, you won't have trouble signing up new policy holders.