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Of course they do!
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They used to be. Until the U.S. Government replaced them with drone replicas designed to spy on the American public. Founded in 1976.
Two weeks ago, a pigeon flew through one of the glass panes in my garage door, spraying broken glass all the way across my garage. It took hours to find and clean all of the mess. The pigeon left unharmed. This sounds about right.
Impacts with glass often cause internal injuries like concussions. It probably flew away and looked fine but died shortly afterward.