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I think it is because the non-doublebonded Oyxgens have a -1 formal charge and the double bonded oxygens have a formal charge of 0. The -1 formal charge allows oxygen to want to bind. I also think that the double bonded oxygens are often on the other side of the bonded oxygens this could contribute to why they don't contribute to the coordinate complex.
Also, the doubly-bonded oxygens are part of a carbonyl group, which is a very stable group that does not want to accept more electrons. A carbonyl group is a carbon atom double bonded to an oxygen with two other atoms bonded to the carbon via single bonds.
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