A good insurance agent/company wouldn't screw you over.
Never had to deal with an insurance claim, huh?
Don't most policies guard against natural disasters/acts of God? I know mine does.
I'm licensed, by law, in the State of Michigan to quote, bind and take premium for auto, fire, life and health insurance. I also handle MANY claims. I work for a great company. We never try to be the cheapest, we try to be the best. All of the people looking for the "cheapest insurance possible" end up excluding coverages they SHOULD have. It's really THEIR fault. Yes, that's not the case all the time. But you wouldn't believe how many people just want the cheapest insurance they can get. Flood insurance is incredibly tricky. I do NOT know New York's law for flood insurance. I know there is Federally mandated flood insurance that you CAN purchase if flood insurance is not offered in your area normally. There are catches, either premium or number of days you can have the policy before you can claim a loss, but it varies.
It's amazing to me how many people try to save a couple bucks a month and end up excluding coverages. If you need to make a claim (statistics show most people make claims - not all are catastrophic), you generally haven't paid enough in to really get the money for the claim. Example: I carry 100/300/100 (all in thousands) coverage on my automobile. Michigan law has liability coverage minimums at 20/40/10 (thousands). The cost difference is literally $2-4 a month. But, if I get in an at fault accident and put someone into the hospital and their bill is $98,000, I'm covered. If I had 20/40/10, they could sue my ass for the $78,000 that I wasn't covered for. Sure, they may never get that much, but their insurance company would have no problem garnishing my wages to cover the bill.
Also, if the insurance agent did not accurately go over coverages with the insured, and they didn't realize they weren't covered, they can sue the agent for that. Usually agents have errors and omissions insurance to cover for this. But, if it's a legitmate "my agent didn't explain this and now I'm fucked", you can still get your money to cover your claim.