Our bottleneck may be training times, but psi skills only barely have an advantage there. The second dot of an ability is only 1 week. With a tutor, it's exactly the same cost and time as the second dot of a psi skill. The first dot will take longer than the first dot of a psi skill, but I think it's worth it.XP is not our bottleneck for training, it was always the training times.
3 whole weeks for Socialize 1 is already a sizeable investment, forget talking about taking longer. Compare that to new Psionic Skills only taking 2 weeks (reminder that weeks assume 8 hour days which Amu doesn't get, she gets maybe 2-4 hours typically depending on stunt, so in practice you'd be doubling or quadrupling the week count).
Personally, I am highly unconvinced that Socialize is worth training over the whole array of Psionic Skills or the defensive Abilities like Integrity and Resistance, or even Occult and Medicine. And especially since the QM is hinting that Midori's own Socialize rank is probably at least 3 or 4 (since it's "easily" higher than necessary to act as her teacher) meaning that if we ever needed it, we could probably throw her at the problem instead of Amu.
We can't rely on mom to have all our conversations for us. Most of our conversations happen without mom around. Plus, people who want to have a conversation with us will go to us, not mom, and we won't always have the luxury of fobbing them off on mom.
Social skills are extremely important, and everyone needs their own. I'd like ours to be competent.