Why do cable disk brake instructions say not to use the barrel adjusters? Most instructions that come with cable (aka mechanical) disc brakes say not to use the barrel adjusters on the brake levers.

Why not? Is there that much difference between the barrel adjuster on the levers and the barrel adjuster on the calliper?
As you dial out the barrel adjuster on the brake lever you pull more cable by effectively lengthening the cable outer (aka cable housing). By pulling more cable you change the starting position of the caliper brake arm, which if extreme enough, could mean:


the caliper brake arm may not have enough travel to get the full braking power; and, 
If the caliper has some sort of progressive engagement trajectory, you start the contact point at a later point in the curve. (This was noticeable with early Shimano mechanical disc brake calipers, which would  loose initial brake bite.)


Either or both imply you are operating the brake outside of the intended design parameters, which means that the functioning can be negatively affected.

Adjusting pad engagement by using the adjustment knobs on caliper keeps the caliper brake arm in the same relative position regardless of pad wear thereby maintaining brake function throughout the life of the pad.