FTA "To fly a parabola takes 3 pilots working in concert. Two pilots sit in front of the control columns and a third sits in the center jump seat to manage the engines. When flying a parabola, one pilot is responsible for the pitch of the aircraft and the other for the roll. The pilot responsible for the roll of the aircraft actually has a modified control column in order to put as little pressure on the yoke as possible, allowing the pitch pilot to focus on the correct parabola timing." I think precise timing requires many pilots. Lots to keep track of in the name of science.

My aviation family has a long history all the way back to training pilots for WWII (already highly experienced - too much so for combat) so my hunch is accuracy and redundancy.

Under normal conditions, sure it’s a one time maneuver, within limits, etc. This is much more of a risk-laden undertaking with the repeated stress on the airframe, the human body, and so having individual attention on important individual tasks - with experience and brain computing speed machines still can’t match for a brilliant stick and yoke pilot in unexpected conditions - this is for safety.

Also considering my background with French culture, I imagine the discussion went something like “we could do it with fewer personnel, but why? This works.”

I imagine it's for an abundance of caution, as they are flying these planes way outside what their normal operations manual recommends. I assume a 320 NEO or a 737 MAX would slap the hand of the pilot if they attempted to go for a +50 degree climb and scream expletives in the voice alert system.

Yeah let's put Musk's autopilot in it and lose 20 people every few years when the plane get scared by the shadow of a cloud. That'll save money