The Constitution says what the federal government can and cannot do. It doesn't say what the states can or cannot do internally because, at least at that time, the federal government had no power over the states (literally - the Articles of Confederation had virtually collapsed by time the states decided they needed a better plan). Article 4 does describe the relationship of the state with the federal government and other states. In other words, the Constitution only gives part of the picture, not the whole picture, when it comes to the states.
When it came to militias, Congress could:
To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress
And the President:
The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States
The militias (which evolved into today's National Guard) belonged to the state. The federal government had power over the militias only when they were supporting the federal government.
The Constitution doesn't actually describe how that transition takes place and that might be seen as a weakness seeing as how states were also supposed to donate troops under the Articles of Confederation - but didn't. When states requested help from the federal government, such as during the Shays Rebellion in Massachusetts, the federal government under the Articles of Confederation couldn't come through for them because the US Army only had 625 troops and there was no power to force states to turn over control of their militias to the federal government.
There was nothing in the Constitution to directly rectify that problem except the good faith that states would be more willing to support the federal government if the federal government was better. The Constitution did allow the federal government to have its own army and navy, with the size unspecified (but hopefully larger than 625).
And the federal army did eventually gain true power over the mlitias, at least during war time, shortly after the start of the Civil War when the traditional relationship was blamed as contributing to several defeats to start the war off even though, per the Constitution, they should have had that power right off the bat once they joined whatever military campaign the federal government was fighting (never mind that the Confederates had an even less centralized military and their lack of centralization persisted throughout the war). It took a while for those two clauses in the Constitution to actually mean something.
Trivia: The founding of the National Guard dates back to Dec 13, 1636 - 140 years before the Revolutionary War.