The order that puts alaf first is older than any script that uses it, and it is one of the most conservative facts in the history of writing. Abecedaries, practice lists of the signs written out in sequence by learners, survive from sites across the Levant, and they show the same run of letters in the same order that a Samaritan child is taught today. Nothing about the sequence follows from the sounds. It was inherited, and every alphabet that borrowed the signs borrowed the order along with them, adding whatever new letters it needed at the end rather than in the middle. That is why Greek alpha, beta, gamma tracks alaf, bit, gaman, and why the letters Greek invented for itself sit at the back behind tau.
The order does real work rather than merely recording a habit. It fixes the numeral value of every letter, so a scribe numbering the sections of a manuscript is relying on a list nobody chose. It underwrites the alphabetic acrostic, the poetic form in which each unit of a poem begins with the next letter of the alphabet, which is only possible where the sequence is fixed and known to everybody. And it is the frame the letters are taught in: an alphabet is recited before it is read, and a community that has kept a script in use as long as the Samaritans have has kept the recitation going beside it.
What the sequence does not carry is meaning. The gloss attached to alaf, an ox, is argued backwards from the letter name rather than recorded by anyone writing the script, and the atlas marks it as a modern reconstruction wherever it appears in the Northwest Semitic alphabets.