All insurance co's suck....there, I said it
!!!
My properties' rates went up almost 50% a couple of years ago...I've never filed a claim, ever. Ins. co's do NOT lose $...they are recoupng payouts from coastal storms and include my area due to wind...
As far as trees go....if a healthy tree falls due to wind, ice, etc. then each property owner is responsible....at least that's how it is here in NC.
Your healthy tree falls on his property/house....removal/damages to his house, etc. are his expense/insurance.
Healthy neighbor's tree falls on my side, then it's mine to incur ( or my insurance) if it hits a structure.
An an obviously dead/dying tree is different....give notice, take pics, etc. because negligence enters the equation.