Trees are self optimising structures and will shut down dead branches allowing them to fall off naturally, however this isn’t always practical meaning intervention is necessary.
Deadwood removal over public areas or structures is an important tree management task, again requiring a skilled and knowledgeable approach .
As a footnote dead wood removed from a tree makes for a great habitat for important insects and ground mammals, small piles of dead wood are a great addition to a wilder area of a garden .