Not Quite - only if risk is spread across the whole pool does it provide the value you describe.
If risk is assessed perfectly, they know that Alan's & Charles' houses will not have a fire, but Bob's house will burn. Alan and Charles (and all the others) pay only the $0.25 overhead/profit, while Bob must pay the $125,000 ratings +profit.
Insurance basically disappears, as it adds no value, and we go back to being self-insured.