The reason the team uses the 6.5 is to make easier to coach and call dope. If they all shoot the same round at same velocity window corrections can be done much more quickly.
Here's an article with people with vastly more experience. They are doing a straight comparison with the 6br family. Throw in the bigger faster 6's that push to 3300 fps and they can hang with the fat 7's without the price of recoil
My experience in center fire was limited to a few matches a year no sooner than 18 yrs ago. I did however compete in sporting clays quite seriously. The benefits of less recoil were crystal clear. I started with heavy trap 1 1/8th load. By the time I stopped I was using 3/4 oz loads I didn't do well until I shed the recoil of the heavier loads. I was lucky enough to win my state championship 3 times. The faster loads with less recoil allowed me better target concentration. In shooting the more you can control you sub conscious the better. You keep beating yourself with recoil your brain will pay you back at the most inopportune time.
The main reason I say this is I developed a detached retina from shooting. I had it fixed but I cannot compete at the level I once was at. If I can pass on just one thing to prevent that from happening to someone else I will do whatever to do that.