The reason for needing an Amendment, the District Clause in the Constitution making it the seat of the federal government. Which due to the separation of powers clause (state-federal), the District cannot be a state unless the District Clause is removed from the Constitution through Amendment.
If you research the Constitutional Convention and debate in Philadelphia, you will find agreement amongst the delegates that the "District" was established to be the seat of the federal government and not within the boundary of any one state to ensure the clear separation of powers. There was little argument amongst the delegates regarding this matter.
When the Constitution was ratified, state governments and the federal governments were viewed as equals. The Supremacy Clause, as written, interpreted and adopted at the convention, did not elevate the federal government above the state. The Supremacy Clause merely granted specific powers to the federal governments. Those powers not specifically delegated to the federal government, remained with the states.
Perhaps the most significant case regarding the Supremacy Clause, Ableman v. Booth, 62 U.S. (21 How.) 506 (1859), whereby SCOTUS ruled that federal courts, not state courts, determine all matters concerning interpretation of the Constitution.
IMO, any action by Congress to make the District a State will be swiftly appealed directly to SCOTUS. And in rare cases, such as Bush v Gore, SCOTUS will likely be inclined to take this case under consideration without it first moving through district and appellate courts.
And with Chief Justice Roberts joining the liberal justices on some major decisions the past week, I wouldn't wager on what his decision might be regarding statehood for the District. While he was once a strict constructionist, he now seems to favor current social interpretations of the document.
You might be wondering if I'm a historian...
Nope. But my mom was an expert on American history. She had her PhD in American history, emphasis on the revolutionary period. By the time I was 13, I had visited every significant and insignificant revolutionary battlefield. Further, she could walk through Independence Hall and describe ongoings, who state where, allegiances amongst delegates, as if she had been there.