"For an appeal to be successful you have to prove the selection criteria was not applied correctly"
That is more or less the only grounds for a successful appeal when Infant Class Size rules apply (up to and including Year 2, maximum 30 pupils per teacher), when you need to show an error in processing your application which cost your child a place (eg child placed in wrong category, distance measured wrongly). You don't need to identify who benefited from this error when you appeal.
The other permitted grounds for ICS are entrance criteria which breach the admissions code (eg giving priority to a group they are not allowed to prioritise) or a decision so unreasonable, it is perverse (in a legal sort of sense, so things like child protection issues).
All those apply to KS2 and secondary appeals too.
But when ICS rules no longer apply, you can also appeal on 'balance of prejudice' which means you need to demonstrate that the detriment to the school in admitting another pupil is less than the detriment to your child in not going to that school. That can cover quite a range of stuff - so a demonstrably musical child might win an appeal for a school with orchestra, choirs and musical enrichment programme.
Things like convenience of travel to school however don't play a part, unless the pupil has specific mobility issues.