In landscape parlance a dead tree is a SNAG.
MOTHER NATURE is not wasteful.
Dead & dying trees are equally important as living trees. Maybe more? Dead & dying trees attract insects & fungi which attract song birds. Earth's eco system, a portion.
If a dead/dying tree isn't a threat to safety keep it.
Above, my red bud tree, SNAG, lasted 6 years. It danced with the birds outside my breakfast room window during that time.
Who knew, dead & dying trees are precious.
Garden & Be Well, XO Tara