It's normal for super villains to take one million extra steps to reach a simple goal. Pigeon Woman, however, moves monuments by hypnotizing vermin, which equals out to one million steps taken to accomplish absolutely nothing. Also, Pigeon Person seemed really upset about Robin calling her Pigeon Woman. Maybe she has a dong?
Ah, I'd still hit it.
The above panel is the only explanation of Pigeon Woman's plan we get: "An America without statues is an America without a past." Even if that was remotely true, what? Is her plan really to rebuild America over the remains of its forgotten, statue-less past? Is she hoping that we'll all go, "Wait, where are all the statues... w-what is this place? Maybe even, who am I!? Oh, hi lady... I-I mean "person." I see you like pigeons. Will it be you who leads this brand new country?"
This plan is of course, nonsense. Maybe she'd collected so many pigeons that they'd run out of things to shit on and she was too embarrassed to tell Batman that that's why she was stealing the Statue of Liberty.
Fortunately the Army saves absolutely nobody by using tax payer money to help Batman drop cup cakes to distract the pigeons.
This somehow proves the cupcakes are delicious, even though pigeons get excited when they find a wet napkin in the trash, and would eat disease out of a hobo's hand.