Alphabets may only have been invented once, but writing systems that have a (roughly, it's never perfect) 1:1 correspondence with the sounds of the language have been invented several times independently, e.g. in syllabaries (Japanese Kana are derived from Kanji) and abugidas. I would suggest that that conceptual leap is a much bigger one than the one of treating consonants and vowels as independent.
Syllabaries have been invented multiple times independently and an alphabet only once, which to me would suggest the alphabetic step is the harder one to make.
Why would you suggest the opposite? I'm a complete layperson in this area, so I understand my view might be quite limited.
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.