Deadwood might look good now but it's a real risk for the whole tree's health. @noah_brown has a point about bugs, they can move from dead parts into healthy wood fast. Letting that rot stay up there invites disease that can kill the tree from the inside. The birds are nice but a sick tree is a huge hassle and cost to remove later. You might end up with a bigger problem than a quiet yard. Why risk losing the whole tree for a few birds?