Back when I was a falco noob, pillaring referred to shield pressure (dair -> shine on shield). I know that isn't the popular definition now, but this old man will respond to that definition anyways.
Falco's shield pressure is not as good as people think. Its mostly because of his jumpsquat, which is 5 frames compared to fox's 3 frames. Doing frame perfect double shines is basically the only choice he has, with everything else being mixup (shine grab is pretty strong, but he lacks a single throw to combo with). If fox shines out of shield, he will beat your fastest aerials. Sheik can nair out of shield before your dair comes out. Thats why you see literally only westballz being successful as an aggressive Falco (and he plays fox as much as falco now).