One advantage of logic + deduction is potential clarity ahead of time about what the system might do, and ability to explain its actions. If AI safety is your top concern, those seem at least potentially valuable even when other techniques can build powerful systems sooner. (I wish more conventional software had that kind of transparency.)
i'm not particularly fearful of an AI apocolypse, but i couldn't agree with that more.
I have no issue with probabilistic state-space search.