I understand that view Cyc and its not one that I completely disagree with, however I do think the blanket ban is over the top. I think most (if not all) jockeys wouldn't remount a faller unless they were sure that the said horse was fine, and I do think that in sport you need to give responsibility to the participants and allow them to make the decisions be them right or wrong. I am not saying that we should remount horses, rather what I am saying is that a blanket ban on it is unfair on those who unseat at the last fence and/or those who slip up etc and are fine to continue. I think its the same as in the flat code where if you cross the finishing line in a false start you are not able to rerun. Its not flexible enough.
If a horse falls or slips there is always the chance that to continue running may cause a minor problem to become serious and I doubt very much if jockeys would be able to tell. Even a vet could say the horse is OK; but continued exertion may change that. I know that from experience and had we listened to the vet our horse would have been finished. If the jockey has just fallen off then I can't see why they aren't allowed back on. However, isn't it just a case of Rules are Rules. For instance, in show jumping 2 refusals (3 in some events) is elimination, falling off is elimination. It's not essential that Rules are the same in every country. Providing the rules are clear I don't see what the problem is.
This reminds me of dear old Lord Oaksey's famous remark that 'there are fools, bloody fools and men who remount in steeplechases!'. I must admit that the act of remounting certainly used to make me wince as in no way is a cursory glance by a jockey (who himself may not be in his 'right mind' following a thunderous fall) at a horse enough to establish the animals true health and wellbeing. I don't agree with a lot of BHA decision but on the remounting issue I personally think they got it right.