I’d prefer it to extend to all punishments as well – however there are practical considerations that make that awkward. It basically comes down to numbers – the appeals process in this school can handle the amount of appeals generated by corporal punishment. If we applied that process to (say) detentions – which occur at roughly five times the rate of corporal punishment, logically we’d expect around five times as many appeals. As a practical matter, that type of volume can’t be handled – but see below (there’s a difference between formal and informal appeals)
I would not generally expect a student to accept a non-corporal punishment before I would hear an appeal. The quote you’ve given here isn’t really in reference to what I would refer to as appeal (which to me, means a student is asking for a punishment to not occur or be lessened on the grounds of innocence or some mitigating factors).