A guaranteed level of safety basically. We do compete unaffiliated - mainly with pony club which also has strict safety rules, although they are not always stuck to! There are some great unaffiliated venues, and affiliated venues running unaffiliated events. But there are some less good too. You need to know the fence is fixed correctly, ground pinned where suitable. Frangible pins etc are relatively rare at lower levels - but there are other safety measures in place. Jump judges who know what to do in an emergency, and good first aid cover. Eventing is never going to be a safe option. But why place yourself at more risk than you need to. (Although having said that we hunt too which is far from controlled!)
As Shay says we event affiliated because you can guarantee a quality of build for the jumps, the course will be to the stated height and whilst there may be appropriate technical challenges they are going to be planned like that rather than 'traps'. We do Hunter Trials but only those where the quality of the course is guaranteed I do not want my boys jumping over unfixed jumps made of pallets etc. again we hunt but that's the risk I am prepared to take.
I used to affiliate but have not for the past two seasons for various reasons. I think I must be lucky where I live as I have so far managed 4 unaffiliated events run at affiliated venues (and have noticed no difference from when competing at these venues affiliated previously) I have another 3 events in the diary, again all over affiliated venues but competing unaffiliated. I guess some people are not as lucky with location but for me, especially as I am pottering around at 90 with a youngster there is no incentive to affiliate BE. I have however affiliated BS, as I find unaff sj round here traumatising and also enjoy the lure of prize money ))
I was just curious to see why people do, I'd love to do it someday but have always felt I need to be better than I am. Avthechav I wish we were as lucky, all affiliated venues are at least an hour and a half away we don't actually have any affiliated BE events in our county (Durham) which is massively annoying haha