I guess this is where I assumed that the '..only aikido will help aikido..'assertion was made. I can't quote chapter and verse for studies that have shown improvement of performance but I can leave references.
No question that secondary activites can be used to improve performance in primary activities. Be that as it may, to improve preformance for an activity, the majority of training time should be spent on the specific activity. Football players are best served by playing football, by engaging in running drills that improve football performance, by using strength training protocals that mimic and benefit football performance, by choosing a nutritional program that supports football, etc....
So, yes, a football player will run, will strength train, etc. to improve their performance. But the majority of a successful football player's time is spent in football specific drills and secondary activities are geared to improved football performance. Which, as I understand it, is what you're asserting. (Please correct me if I've misinterpreted your position).