Tons of empathy having travelled w. twins from 10 mos. to 8 years now. But, no sympathy. The captain's decision is safety based and has nothing to do with anything else. The consequences were terrible, but the captain's decision can't be based on whether there is hourly or weekly service.
What if the kid had been flung from her seat during a turbulent climb out and seriously injured? What if she had been flung and not injured, but had seriously injured another pax? (30-40 lb. projectile).
If this happened to me, I'd be upset, but not at the carrier.