It's perfectly reasonable, and expected, that insurance requires you to mitigate any further damage from an event (your "rot caused by roof tear" example). If you get a roof tear and water gets in, as long as you address the situation quickly the repair will include drying the water intrusion to avoid rot. And, with the terms you gave, that could include replacing water saturated wood (it wouldn't have had time to rot). They're just not going to cover it if you only realize/claim 6 months after the fact and it's too late.
I'll sell you a policy which covers all hazards and also allows you to be negligent with maintenance/repair. How much coverage do you want? Add 10% and send me a check. Coverage is limited to a single claim.
