YOu'll end up with double coverage on the house. If house is destroyed, who gets the money? If the mortgage company is escrowing your insurance, then they shouldn't be makeing you get additional coverage. Imagine if you get your coverage from the same company, and you both try to file a claim for the same "damage".
Something doesn't sound right to me. In my home ownership I've had both the insurance escrowed and self paid. In both cases, I chose the insurance company, and when necessary filed claims and had repairs made. If the house were destroyed (hasn't happened), I think, the mortgage company would get a check for the coverage amount and refund me anything in excess of the balance due. Or I'd get the check and still be liable for the mortgage. Don't remember which way it is written.