Cappon magro is a Genoese dish whose reputation rests on unusually elaborate construction. It is not a casual toss of leftovers but a composed plate in which boiled fish and vegetables meet salsa verde, so the first reason to care is the ambition of the assembly itself.
The documented Genoese preparation keeps those boiled elements together with the green sauce, which is why the dish reads as architecture rather than a simple salad. That pairing is the material story: fish and vegetables cooked until they can be arranged, then bound by salsa verde into something far more considered than its humble parts suggest.
If you meet cappon magro on a menu or in a Ligurian conversation, treat the name as a cue for that unusual elaboration. The useful takeaway is to look for the composed Genoese character rather than a quick mixed salad, then follow related Genoese seafood and vegetable dishes that share the same appetite for careful building.