That would not be the result.
For example, on abortion, many states would ban it.
In contrast, right now the legality of abortion is decided at federal level and so it being legal is forced on all 50 states.
Abortion isn't the only thing Paul has said this on. Paul has made statements in the Heller case that the Feds have no authority to protect your 2nd Amendment rights from State regulation and he said it in the Kelo decision where he believes State governments can confiscate your property without due process of law.
In Paul's world, you might as well throw out the Constitution.