Huh! I'd always accepted the backronym without even thinking about it, but it makes so much more sense as arbitrary letters associated with sequences that are very easy to remember and distinguish than as a real weird acronym that just happens to have that property. You have reorganised my world in a slightly more reasonable way.
Interestingly there were competing distress signals at the time, but I guess SOS won because of its usefulness outside of morse code. As you mentioned, it's easy to remember, the letters are distinguishable and it also works upside down when written.