Thank you Jacques for some interesting information.
It may be useful to ask why it is necessary to have an order to the
letters. It is not obviously necessary for writing (I don't have to
keep thinking about alpha order as I write), but it is essential for
teaching because young (mostly) minds need something to hang their
learning on. The old Irish alphabet was mnemonicised (?) as the names
of trees (although of course the order was fixed exogenously to
this). Might it not be something more like the need to have a sequence
that was easily memorable (at the time)?