For natural pg you can wean yourself off of it sooner than that. The issue is that you want your blood to be not super "clotty" when the bean is trying to implant and the baby aspirin can thin your blood. It may help the bean burrow into your uterine lining.
It's not so much that you get addicted to it, but that you need to give time for your body to adjust chemically rather than just stopping it. If it needs to produce more or less of some chemical as a result of you stopping the aspirin, you need to give it some time to do that.