Yes, but in most cases private insurance companies do not charge high rates for flood insurance, they simply refuse to provide flood insurance. The issue for them is that floods tend to affect EVERYONE in an area (or no one at all) and so the losses due to claims cannot be averaged over a large customer base and thereby kept consistent from year to year. This creates a kind of risk that wise insurance companies will not be willing to take on.
That is not to say that there is NO price: as an extreme case, an insurance company would be willing to sell a policy for flood insurance for an annual price of the full replacement price of the property. (Because they'd be guaranteed a zero or positive return in the first year.) But that's not what we traditionally mean by "insurance", which involves the concept of sharing risk over a broad pool so that each member pays for the average cost rather than risking having a high cost.
That is not to say that there is NO price: as an extreme case, an insurance company would be willing to sell a policy for flood insurance for an annual price of the full replacement price of the property. (Because they'd be guaranteed a zero or positive return in the first year.) But that's not what we traditionally mean by "insurance", which involves the concept of sharing risk over a broad pool so that each member pays for the average cost rather than risking having a high cost.