My pigeons, in cage, and free flying, regardless of breed, eat a wide verity of insects. insects being base proteins n a lot easier to break down, full of much more proteins etc than "animals". I've never seen kidney liver etc probs from insect eating in necropsy, n a neighbr down some way years ago had tumbler type pigeons he really didn't take care of, so the pair became resourceful and ate roadkill even aside from mostly insects they fed on (maggots were their fav) also attracted to bodies when warmer (they also fed on other birds of his that died).
mine being fed well still seek out bugs on ground etc n on the wing. Enough proteins in way of peas,saflower, sunflower hearts, and uncooked unsalted peanut hearts, and much more, are all around probably better than feeding them insects if they do not have access to them (mealworms etc during breeding n rearing time). cooked domestic people food is really bad for them seeming as seen some do, as well as dogfood not too good for, but some racers feed to their breeding n rearing birds. I've found mine will eat dry kitten kibble if i don't stop. My pigeons regardless if getting fed higher protien at time, frenzy out of reflex now, even if isnt any feed or theyr not hungry, it becomes reflex. feeding higher protein feeds can make mating wannabe birds act aggressively supposedly.