whose sport doesn't routinely cause brain damage, like basketball players?
Basketball is a contact sport in which players are routinely jostled around, whacked with stray limbs, and falling to the floor. Plenty of people in basketball suffer concussions. Just ask Joel Embiid. An unstudied sport is not a safe sport. When the data is complete, there probably will be few sports unaffected by CTE -- especially team sports. Once this problem is fully understood, parents and their kids will have to decide how much additional risk they are willing to accept. It will probably have to be more than zero, unless they are really into tennis, golf, and swimming.
I do agree with your overall point that the control group should be as much like NFL players as possible, without bouncing their heads around. They should be much more wealthy, famous, and physically fit than the general population, as all of those things influence suicide rate. Good luck finding that group, though.