One reason for using chicken thighs is for the uniformity in size. Judges like to see that in a turn in box. If you have instructions to turn in 6 pieces of meat per box you know how many thighs you need to turn in. If you turn in chopped chicken breasts and not all judges get to sample your entry, then they judge you harder per the KCBS Rules.
Here it is from the KCBS Rule #16:
Rule 16
Each contestant must submit at least six (6) portions of meat in an approved container. Chicken, pork and brisket may be submitted chopped, pulled, sliced, or diced as the cook sees fit, as long as there is enough for six (6) judges. Ribs shall be turned in bone-in. Judges may not cut, slice, or shake apart to separate pieces. If there is not enough meat for each judge to sample, the shorted judge(s) will score a one (1) on all criteria, and the judges having samples will change the Appearance score to one (1).