In terms of sheer game-theoretic value, sure, perfect knowledge will reduce value gaps. However, the thing with having your house insured is that you will have

In terms of sheer game-theoretic value, sure, perfect knowledge will reduce value gaps. However, the thing with having your house insured is that you will have somewhere to live if you have a house fire. The +/- for the insurer might be close, but going from having a house to having no house is a bigger deal than going from one house to a twice-as-expensive house.