Each IAP is a "separately constituted legal entity" and entitled to take its own (well-reasoned) decisions.
I can give a view, based on panels that I have sat on.
If a child appealing against non-qualification was successful in that part of the appeal, would the fact that they live very close to the school, and would undoubtedly have got a place had they passed at the correct time, hold very much weight in the oversubscription part of the appeal?
Living very close is worth a mention, but the unfairness of the system probably won't count for much.
How will a panel weigh up the different factors? - some children may have extremely high scores but live a few hundred yards further away than the last child to get in; others are well suited to the school's specialism; others have social or medical grounds or an allocated school with very poor results.
In my experience, very strong medical/social reasons tend to be the most persuasive, if substantiated.
Q&As, C2 g. "There are strong medical or social reasons why your child needs to attend this particular school. These are often the most compelling reasons, but you will need proof, and you will need to demonstrate convincingly why only this school is the solution
Next I would put strong educational reasons.
Q&As, C2 f. "There are strong educational reasons (I don’t mean a preference for a type of school such as a grammar school – I mean something specific on offer at this particular school which is not available at any suitable alternative. You would need to prove why this is so crucial).
I wouldn't normally take account of the score, because everyone who has qualified has qualified. However, there could be some exceptional cases that are compelling (e.g. maximum possible score, but worst possible school allocated).
Last I would put siblings, distance, transport/logistics, in-catchment, etc.
If I've put medical/social at the top of the list, this is only because I've found these cases to be the most successful in practice. It's possible that the very strongest case at an appeal might be based on something else. A very strong case is like an elephant - you recognise one when you see it.
Each case has to be considered on its own particular merits. Appellants sometimes have a combination
of the points mentioned above, which, taken as a whole, can add up to something really compelling.