hi,
you aren't missing this. Show duplicates is NOT a tool to allow to simply select all and hit deleted. It is showing you the duplicates, one beside the other, to allow you to discriminate two songs having the same name but that may not be duplicate. For exemple, they may be two different version of a same song and that you want to keep them. For this reason, automated process are somehow risky to loose also song that you want to keep.
however, if you still want to proceed with an automated script, you can find some at
http://dougscripts.com/itunes/.
Personnally, I would still discriminate duplicated songs manually by reviewing the list of "show duplicate" to avoid deletion of song I wish to keep. I also have a quite large library and found many songs having the same name and not being duplicates.