"If the Constitution can mandate eliminating badges and incidents of social injustice X, then the rest of the Constitution can hardly forbid eliminating “badges and incidents” of social injustices Y and Z, by legislative means. That’s some serious penumbra, shaping up. Or am I missing something ?"
He sure is missing something. The Constitution can do whatever it wants (except depirve states of their equal suffrage in the Senate).
Look the Constitution clearly allows amendments to do anything (except deprive states of their equal suffrage in the Senate).
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
I think that quotation clearly answers Holbo's question. Sure it can. There's nothing about badges and incidents of social injustice X Y and Z there.
There is no need for an amendment to not contradict the rest of the constitution. The 21st amendment contradicted the 18th amendment, yet it is a valid part of the constitution. The 13th amendment contradicted the clause that said that slaves who escaped to free states remained slaves and had to be returned to their owners. If an amendment contradicts the pre-existing constitution, then it cancels and nullifies the bits it contradicts.
Just to avoid giving any aid and comfort to libertarians (who don't give a damn about my aid and comfort) I note that I believe that any constitutional private property rights that might ever have existed in the USA were eliminated by the 16th amendment. The power to tax is the power to regulate. The power to tax income from any source derived (not necessarily at the same rate) is the power to regulate anything that has anything to do with income. Yes the income tax is clearly forbidden by the main body of the constitution and by the 5th amendment. So what. It is exactly as unconstitutional as "intoxicating liquors."
A ten billion percent tax on revenues from operating a racially discriminatory business (say a snack bar where African Americans are denied service) would be much harsher than the civil rights act and clearly constitutional. Note I said revenues not profits -- the 16th amendment does not establish a definition of income and say that it must be net not gross of costs.
Can the constitution ban some discrimination and prevent congress from banning other discrimination ? Of course it can. Consider the 14th, 15th, 19th and 26th amendments. The 15th said suffrage could not be denied to men over 21 on account of race, women were still not allowed to vote. State legislatures maintained the constitutional power to decide if women could vote. A mere law passed by congress and signed by the President which mandated women's suffrage (at least in presidential elections) would have been plainly unconstitutional : "Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress ... ." Even now states can deprive felons of the right to vote.
The main body of the constitution forbad a religious condition for holding office "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." but said nothing about race, gender (or height or weight). It is clear that state legislatures had the authority to declare that their electors in the electoral college must be female, or over 6 feet tall, or anything they want which doesn't involve religion. If congress and the president passed a law attempting to over rule such nonsense, that law would clearly have been unconstitutional.
The constitution is under no obligation to be elegant or harmonious or philosophically (as opposed to logically) consistent. What would such an obligation even mean ? If the constitution can't do something, that means that some court can find the constitution unconstitutional. Can you even imagine such a [non]constitutional order ? If you can, could you will it into being ? It would make the USA an oligarchy ruled by the supreme court of the day.