The Sanskrit letter table is made to be said aloud, and its structure is what makes that possible. The vowels come first in a fixed order of pairs, then twenty-five stops arranged in five groups of five, then the semivowels, the sibilants and the aspirate. Within each group of five the sequence is always the same: voiceless, voiceless aspirate, voiced, voiced aspirate, nasal. A learner who has the rule can recite any group from its first letter, and can name any letter from its position without ever having seen it written.
Recitation of this kind does more than fix an order in memory. Because the arrangement is by where and how a sound is made, saying the table in order is a walk through the mouth from the throat to the lips, and the learner is rehearsing the analysis at the same time as the sequence. A table arranged in the arbitrary order the Mediterranean scripts inherited teaches nothing about sound at all.
In East Asia the recited table travelled better than the written one. It could be taught by voice, checked by ear and carried without a manuscript, and its influence turns up in places the script itself never reached. The Japanese kana are ordered on the Sanskrit principle rather than on any native one, and the standard chart of them is a grid of the same kind, read the same way. The order outlived the letters that carried it.