First-party claims, absolutely. Insurers want to pay when they are liable, and they don't want to pay when they are not. Your contract defines that, and your contract is written in plain English.
Insurers aren't out to get you, and the insurance industry doesn't rely on shafting people to make money. When you purchase insurance your policy is priced according to the exposure it creates, but a lot of people mistakenly assume that the insurer's profit comes from premium payments. It often doesn't. From what I have read, insurers are generally happy to break even on premiums vs. payouts. Their profit comes from investing the float and earning a return on those investments.
Related, I think that most people don't understand how tightly regulated insurance is, and how much it can suck for an insurer to improperly deny a claim. It creates huge legal and regulatory exposure for the insurer.