Of course the role of the SCOTUS in defining the Constitution was decided by the SCOTUS itself, before that the issue wasn't exactly clear on who said what the Constitution said, but the SCOTUS was the natural choice after all since the issues in Marbury v. Madison were of national concern, what other court than the Supreme should hear the case? And the Court decided that it was only the natural choice to decide issues of Constitutional law as issues on the Supreme law should be decided by the Supreme Court. One could argue that the Court was wrong in its decision, but it is a decision that has been in effect for over 200 years.
BUT then you're back to the same issue there was 200 years ago, who decides what the meaning of the Constitution is? The meaning of many parts many be literally clear, such as the 2nd amendment, but we've already shown that literal define is not the same as legal definition. Otherwise the SCOTUS wouldn't have felt the need to define handguns as arms, and thus protected by the 2nd Amendment, in their last big 2nd Amendment case in 2006. Whereas the literal define of arms would obviously include handguns, legally it may not, which sounds crazy I know. Other parts of the Constitution are unclear literally and only make sense with viewed with through the scope of legal precedent and court rulings. And lastly, what if two individuals or two states or two parties have a disagreement that goes to court and the Constitution is cited as a defense? The ruling of that court will set precedent for Constitutional meaning.
Personally I think Article 3 was clear on the SCOTUS having this role anyway, but thats the thing about law is that the wording can change meaning with precedent just like in English common law which our system is based.