Michael, it's a good if somewhat wordy and complex question. I doubt many on this forum could provide an unequivocal answer, indeed I feel the response coming 'talk to your insurer'. However, I have had some dealings with sports and social events so I will try to assist. First, are you providing any people (ie officials, coaches, etc) for these events? If not, what are your h&s responsibilites for these sporting events?
Putting aside RAs for a moment, there needs some assurance that the people running these events are competent, the premises are fit purpose and arrangements are in place for accidents, fire and emergency. Now, this might be via an RA process or it could be by another medium. If you are provided RAs/FRAs they will in all probability be generic RAs, probably not very good ones in my experience. Do you feel confident with a tick in the box?
Notwithstanding the above, how practical is it to vet every competition, premises, people and organisation running these events? Probably not very practical. It may be that you (UK Athletics) develop a proforma for the organisation facilitating the event, asking specific details about security, supervision, premises, fire, first aid and emergency arrangements, number of people the venue is licensed to hold, whether RAs/FRAs have been completed, possibly with a sample...I think you get the picture.