The only way body composition influences program design for me is as it relates to their classification: underweight, normal, overweight, obese, etc. and where the intensity of their program would be initiated. But of course the other parts of their assessment would also factor into that decision.
I agree with Susan. It’s either the BF% is above average in which case your program needs to focus on reducing it or if it’s average or below average then you go by what your fitness assessment showed and what your client’s goals are. Sometimes your client doesn’t care that much about BF%, but instead wants to train for a race or has other unspecified personal reasons why he/she likes to workout. There are so many other factors that come into play as far BF% and program design goes (such as age, medical conditions, dietary restrictions, etc.), that it’s almost impossible to give a black and white answer.