Why is “Congress shall have power to enforce this article by appropriate legislation” necessary?
In the absence of the clause, the intent of the amendments would be delayed until the Supreme Court decided cases affected by those amendments.
The quoted sentence, in some form, occurs in the following Amendments: 13, 14, 15, 18, 19, (21), 23, 24, and 26. [Amendment 21 does not have the quote, but is included here because it repealed Amendment 18.]
Each of the above amendments, in one way or another, are related to rights. Congress has no other expressed legislative authority to protect rights.
The quoted sentence does not occur in the following Amendments: 11, 12, 16, 17, 20, 22, 25, and 27.
Each of these amendments are related to the powers or structure of government.
Expressed legislative powers include:
Article 1, Section 8, Clause 18:
Congress shall have Power ... To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
Article IV, Section 1:
Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.
Article IV, Section 3:
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
[Emphases added in the above.]
[Note that Article VI, Section 2, unlike Sections 1 and 3, has no expressed authority for Congress to make laws, leaving it to the Court to decided what is, and what is not, a violation of privileges and immunities.]
Of particular interest is Clause 18, which may be separated into two clauses to understand its effect.
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States.
To make all Laws which shall be necessary and proper for carrying into Execution the Powers vested by this Constitution in any Department or Officer of the Government of the United States.
Item 1 covers all powers vested by the Constitution in the Government of the United States, including Article II, Section 2 assigned to the President regarding such powers as treaties and appointments.
Item 2 covers the structure of government, in particular, the clauses vesting the legislative, executive, and judicial powers found in the first three Articles.
Thus, for amendments related to powers and structure, Congress has all the legislative authority it needs; for amendments related to rights, Congress had to be granted the legislative authority to give effect to those amendments.