Yeah, there are sort of different requirements for a kilo rider vs a 4k rider. The standing start is crucial for most super strong kilo riders. So, they may like deeper drop bars that don't flex. Because the speeds are higher, they may like wider elbow placement for stability at 65kph/40mph.
I'm not a pursuiter, so I don't know things from that side of the house.
Yes, if you pay a coach, I guess you should listen and trust in the person and the program. But, a good coach will also listen to feedback from you and your son and take that into consideration with his/her advice to you.
To be honest, we are now splitting hairs. There are more factors that we aren't talking about that would have a much bigger impact on a kilo or 4k.
You are sorta asking, "Which bars and which position are best for my son?", that we cannot answer. We can, however, offer our own opinions about equipment that we've used and liked or disliked and the reasons why.