Insurance companies make money by not paying for claims.So private companies will maximize profit by collection premiums and then avoiding paying claims as much as possible. The only appeals to this are to the company itself, to the state insurance regulators (which are staffed either by people from the insurance industry or people who are planning to later work for the insurance industry), or to the prohibitively expensive courts. The Republican Tort Reform efforts are all designed to cut off access to the courts by limiting the ability of tort lawyers to get paid for their efforts.
Christy Hardin Smith has a good article on this subject over at FireDogLake.
While it's not perfect, the solution is single payer national health care with the premiums paid by taxes on both employers and individuals and the crazy-quilt of varied coverages and their administration standardized.
Because there are so many insurance companies, each one can claim that refusal to pay valid claims by a different company is not something they do. The actions of each individual company is concealed in the many different companies all trying to offer different products. No government agency can get away with that. There would be a single system of appeals carefully covered by the media.
Stripping out the unnecessary administrative expenses out of the system would save 10% of the waste, fraud and abuse that characterizes the present lack-of-system. Eliminating the overpaid CEO's and dividends to owners would recover another 10%. Then eliminating the costs of salespeople would save another 10% or more.
We need single payer health care in this nation immediately.