Why is the boot camp for the Survey Corps 3 years long? Because Japanese High School?
The biggest reason for that would be the 3D maneuver gear.

Modern army boot camp is held only for several months because they just need to learn to use guns, knives, close-quarter combat, learn to drive helicopters, tanks, humpvee, etc, which is easy compared to the 3D maneuver gear.

To maintain balance using the 3D maneuver gear even in still position is hard (see Eren's training). Now imagine moving around at high-speed swinging left and right, up and down. People not used to it would throw up. The 3 years are used to make the recruits used to the 3D maneuver gear so that they can move around correctly, because wrong moves means death in the jaws of the Titans.