Even setting aside the arguably much greater ethical and moral issues with such extinctions, think of all the species that could have yielded remarkable and useful secrets to us after proper research -- if they still existed. Sometimes I wonder if by such wanton destruction is sealing its own doom.
Perhaps a cure to a some future cataclysmic disease outbreak might have lain in a formerly living organism that can no longer help us because we killed it off. Or maybe some revolutionary new material could have been inspired by an extinct species, had we only been able to study it.