Parking regs require reps to be considered.
The authority state that 'the grounds and mitigation you have provided have been considered..'. They are not obliged to deal with every point in a response, but to identify the main points at issue.
IMO, they have done so: 'there is no exemption which allows vehicles to be be parked on the pavement [ in the circumstances stated by the OP, namely 'that your vehicle was broken down at the time'].
IMO, you would struggle on this point, but given that their written evidence shows a material procedural impropriety, I wouldn't get too fussed.
OP, you could also have included in the progression of your reps that GSV shows parking on the footway by all and sundry over at leat 10 years. But it's a weird set-up. It looks as if the council tacitly accepts that a length of footway is part of a person's property, albeit unenclosed. Shades of Pereira: In R (Pereira) v Environment and Traffic Adjudicators [2020] EWHC 811 (Admin), the High Court ruled that a motorist successfully overturned a penalty charge notice for parking on a privately owned strip of a footway. The court clarified when private land forms a public path and noted that tolerated trespass or private use does not automatically constitute lawful public access.
But you didn't even challenge the authority on this point.
Perhaps add to contravention did not occur...
I would ask the adjudicator to view the GSV snapshots of the location for 20**, 20...... etc. These show widespread parking on the footway, albeit that it's tolerated/accepted adjacent to property but not adjacent to the carriageway. I submit that there is no such latitude available to the authority and that if it wishes to apply the strict provision and exclude non-legislative exceptions, as in my case, then it is required to do so for all vehicles. It is not open to the council to be selective without legislative justification and transparency.