Ah nice, it seems that the adaptive cubic will make larger pockets? Neither cubic nor adaptive cubic seems very... cubic to me, though. Why is it called this?

Adaptive cubic does indeed make larger pockets in areas that are far away from walls. As for the name, I myself imagine cuboid shapes standing on one corner. Prusa has a great page on different infill types: https://help.prusa3d.com/article/infill-patterns_177130.
The only advantage I can think of for grid infill (that you're using) is that it reportedly makes better flat top surfaces.

I manage a few Prusa printers at a school, and have set the default profiles to use 15% adaptive cubic infill.

I change the infill in the following cases:

• Large decorative item: Support cubic.
• Piece that requires strength: Cubic , 20%, maybe add an extra perimeter
• Very thin & tall parts: Rectilinear
• Thin & flat: Grid

Hm, OK, maybe - I think however it would have been difficult for me to keep it going when it sounds like I am destroying the printer for every layer

I wasn't there to hear it, I might have felt the same :)