Why are the transistors in logic circuits used in saturation region for ON state?
Using the saturated state means the output voltage doesn't depend on small variations of the input voltage. 
Using the saturation region (or triode region for MOSFETs) can result in very low power consumption when the gate is kept stable in the 1 or 0 state.
However, there are logic families that use forward active mode for the output transistors in both 1 and 0 states. For example, ECL (emitter-coupled logic). The benefit of this is that the logic can switch more quickly due to no having to move enough charge in and out of the base region to move between the off and saturated states. The drawback is that ECL is more power-hungry than CMOS when the switching frequency is low.