The Civil War relegated state militias (including today’s National Guard) to irrelevance; the country simply couldn’t have state militias from one region fighting state militias from another (in which one chose the mantle of “federal” troops).
Look back even farther to the War of 1812: Some New England states wouldn’t even fight.
That is why it's alternate name is "The War Between the States"
You had the Regiments of National Guard of the 20th Maine, 69th New York etc, fighting against the 3rd Arkansas and the 58th Alabama.
Those Units were called up and created by the states, granted to serve in the Federal/Confederate Army, but they were state creations none the less.
Also once the war was over those units were disbanded, we had essentially had an Army of Citizen Soldiers, not full time professionals.
The Same System was used for the Spanish-American War in 1898, States forming Military units to be banded together under the Federal Flag.
The REAL nail in that system came with the The Militia Act of 1903 (A Progressive Idea by the way) It was the Federal Government increasing its power at the expense of the States and sticking its nose where it didn't belong.