The concept of pooled risk is sound. It's basically the reverse of gambling- somebody is going to be a big loser, so we all pay a little to mitigate that risk. The problem really stems from how insurance is run.

As soon as you pay your premium, the money belongs to the company, and any claims they pay out is just money out of their bottom line. It would work correctly if they only got to keep an administrative fee and the bulk of your money had to be deposited in a fund for the purpose of paying claims.

The company is still incentivized to not pay spurious claims, because it would deplete the fund, but denying all claims and allowing the fund to grow to billions of dollars wouldn't benefit them, because it's not money they get to keep.

If they were required to publicly post their premiums and information on how often and how much they pay, the competition would be to attract the most customers by walking that fine line of paying every claim you could, because the only way to increase profits would be to increase your customer base.