To eliminate the subsidy in deposit insurance - to make deposit insurance a real insurance system - the FDIC average insurance premium would have to be set high enough to cover fully the very small probabilities of very large losses, such as those incurred during the Great Depression, and thus the perceived costs of systemic risk.
In contrast to life or automobile casualty insurance, each individual insured loss in banking is not independent of other losses. Banking is subject to systemic risk and is thus subject to a far larger extreme loss in the tail of the probability distributions from which real insurance premiums would have to be calculated.