What can I do with destroyed cargo?

It seems my initial assumption was correct: it is possible to turn destroyed cargo into crafting materials.

The option to do so only unlocks after you have connected the "Distribution Center West of Capital Knot City" to the Q-Pid network during "Episode 2: Amelie".

Doing so unlocks the "Recycle" option, which can turn anything (except delivery cargo that hasn't been destroyed yet) into Metal, Resin, or Chiral Crystals.