Problem with all the decriminalised legislation is that "representations", and "appeals" are used far too often for the same thing; they aren't. Only adjudicators rule on 'appeals', everything else submitted against a PCN or a Notice to Owner, are 'representations, ('reps' for short). Even councils commonly get this wrong, so I understand your confusion, but the key point is that representations are submitted to councils and also Transport for London who have a financial interest in the result. Appeals are dealt with by adjudicators who have no financial interest in the result.
By rejecting virtually all reps (sorry !!), they ruthlessly game the system for their financial benefit. This is because on getting a rejection, most people, (like >95%), then just cough-up to get the discount, knowing little or even nothing about the law and regulations that govern enforcement of PCNs. Many people don't even realise it is a civil not a criminal matter and think if they take the matter to adjudication, they'll be charged huge sums if they lose. This is totally incorrect; the maximum possible financial exposure is the full PCN penalty which is payable if one loses at adjudication; there are no additional costs whatever. Some even worry they may get a CCJ. This is impossible in the present system which was very carefully written to make sure CCJs can never be awarded for parking and traffic contraventions involving council PCN enforcement.
The point about submitting reps is that you can only take a case to the adjudicators once you have had reps to the council rejected; that is how the system works.
You also hope that they will shoot themselves in the foot in their reply and this happens more times than you might think. Replies that are complete tosh are commonplace, and then give the basis for an appeal to the adjudicators. Total misstatements of the law are very common, like that for Yellow Box Junctions. Also, if you just roll-over and cough-up, they benefit even more by having to do virtally no work at all to get their money. We call it "Joing the Mugged Club".