A known dead limb is the owner’s problem
Where a tree is healthy, a limb coming down in a storm is generally an act of nature. Where it was visibly dead or diseased and nothing was done, that becomes negligence. On a rental the owner is the one expected to inspect and maintain, and a tenant mentioning a dead branch creates a record of notice.
The damage frequently lands next door
A large tree failing reaches a neighbor’s roof, car or fence as often as it reaches your own. That is a liability claim against the owner rather than a property claim, and the limit on a landlord policy is what stands behind it.
Removal costs are capped tightly
Policies typically limit tree removal to a small stated amount and often only where the tree struck a covered structure. On a property with mature trees, removing one after a failure is frequently an owner cost rather than a claim.