We gun drill the axles on our baja car, and the #1 reason for this is to turn the shaft into more of a spring rather a rigid member. If you know or can get damn close to knowing the maximum shock loading going into your drivetrain then you can build your drivetrain around that number or a number slightly larger (factor of safety 1.2, 1.5, 2...ect). Since you know these loadings you can essentially lighten your entire drivetrain... The #2 reason is the materials used as axles lend themselves very well to being springs. 4340 and 300M even when heat treated to a rockwell C 45-55 are still very very elastic. You wouldn't want to do this with an axle made from 1010, 1020 since you can't come close to reaching those hardness ratings...
Yes the axle will be "weaker" but thats a given... your removing material, but it just depends on what the purpose of the machine is and how lean and mean you want it to be.
Lowering the rotational moment of inertia is a big reason, but considering how small diameter an axle is its not a major reason. Your better to make your axle into more of a spring so it absorbs the shock loading and lighten the components in your transfer case/tranny.