While I don’t know for sure, I’d imagine their criteria is fairly complicated to apply..
When I was teaching Edexcel GCSE music students had to chose performance pieces which were then marked from a fairly ambiguous, fairly arbitrary table of statements about the performance, evaluating all the usual things. Mark’s given to a student were then modulated, based on a separate table which evaluated the difficulty level of the selected piece and then moved the overall mark up or down accordingly. The difficulty table was again fairly large and arbitrary and even with a few years experience it wasn’t obvious where various pieces may lay.
This is then sent off to the moderators who would again adjust your decisions and come back with comments, ie ‘the melody line is indeed difficult but the rhythm in the left hand at that point is simple so it doesn’t overall qualify as ‘significantly difficult’ to increase the mark’. Moderators moderations would no doubt be further moderated internally with calls on respective level of pieces being refined over the years.
So going back to ABRSM, I would imagine they have a similar process, and probably spend a lot of time evaluating which pieces will go in their various books, with various standard tables to collate types and levels of difficulty, various levels of oversight on the process and some level of training of how to evaluate in various different circumstances that pop up in pieces less often. I would imagine that if their WAS a table of criteria they could release in order to aid the free choice piece then it would possibly be only half the story without a lot of notes on how to use it.
This is annoying or course, especially with the free choice piece. In my experience the students tend to chose the free choice piece from some other publication where the grade level is more or less known already from another board, previous specification or has been otherwise evaluated at some point to be of a certain grade. If students wish to chose a new piece then this can be a bit of a wild card of course, and the advice from the ABRSM website is to stick to a similar kind of material for easier comparison, work closely with your teacher (though I imagine you are the teacher here!) and pick something that is a known level if possible… I agree some guidance would be welcomed, though as this level of freedom is a relatively new thing and the existing criteria for evaluating the level of a piece is likely convoluted, and ultimately decided by individuals within ABRSM, it may be a while before we see anything, if at all.