I thought this question was asked (by you) and answered earlier (by the way, this place doesn't give "definitive answers" only "community answers" - none of which should be definitive).
I filled all of our applications in with A1234567890. My rationale for filling in the number even though we aren't "aliens" any more is that - well, aliens can't really apply for a passport, and, since they asked for the number, and only us ex-aliens have one, they must really want mine.
I also figured that by including the number, I might make their job a little easier. By including my A#, they can look me up in whatever databases they might have in front of them, shaving a little time off my passport processing.
Also remember, you only need to include your natz cert on your first passport application - the DS-82 form for passport renewals doesn't require original proof of citizenship (
http://www.state.gov/documents/organization/79960.pdf). An A# is just something they probably want.
Why are you hesitant to fill it in? It's not like trying to hide your social security number from telemarketers - these folks are the government and it's right there on your natz cert anyway.