Any concept of enumerated rights would have been squashed by ultra-broad interpretations of the interstate commerce clause, the general welfare clause, and the necessary and proper clause. We battle those now, and the only thing holding them back is the explicit enumeration of rights.
By declaring a few core rights in plain language, the gov't must recognize that any interpretation of the Constitution must be consistent with the BoR - any interpretation of the Constitution which contradicts the BoR must be faulty and discarded. Example: "promote the general welfare" could be interpreted as requiring one to testify against himself, for what could be better for the general welfare than to know who committed a crime? - but since the 5th Amendment prohibits self-incrimination, such an over-broad interpretation of the "general welfare" clause is squelched.
You nailed it again.