It's the kind of thing that can't be priced (as AIG found out.) The distribution of the default rate is unknown and unknowable (fat tails and black swans and so on.)
Also, if you increased the price of FDIC insurance, banks would need to make greater interest rates, and therefore would need to make riskier loans. You could make FDIC insurance contingent on taking less risk, but that sort of regulation always seems to backfire. (Of course we already have such regulation, the article even alludes to it. But increasing the strictness of risk-taking regulation would just solidify the major players.)
Also, if you increased the price of FDIC insurance, banks would need to make greater interest rates, and therefore would need to make riskier loans. You could make FDIC insurance contingent on taking less risk, but that sort of regulation always seems to backfire. (Of course we already have such regulation, the article even alludes to it. But increasing the strictness of risk-taking regulation would just solidify the major players.)