If you intend to be full pay, then you don’t need to apply for aid at all. That is your family decision. Some families don’t apply for aid at all. That is fine.
The tip for being full pay isn’t that huge. But it can be a help with admissions. Your kid needs to still be in the ball park for acceptance.
For schools that are need blind for admissions, the admissions folks won’t know if you even applied for aid. I know there is a little box on the common AP, but really, it’s the financial aid applications themselves that are how you apply, not just that little box.