The alternative possibility is that alphabets lend themselves much more naturally to adaptation for other languages, and so, once invented, they spread extremely fast - faster than it would take for another one to appear naturally.
Yes, that's a nice point - this adds censoring to our "data" on other writing systems. My intuition is that even if you accounted for exposure to an existing alphabet, the time-to-develop alphabet would still be much longer than for syllabaries or other writing systems, but that's a guess.