Among less popular birds, sandgrouse, rails and tinamous are easy to breed in human care. The only reason why they are rare is that other groups are more popular (pigeons, pheasant).
One group not common in collections are Arborophila partridges. The reason may be the call of many species - like banging pieces of metal together.
I don't think call matters necessarily... Many gamebirds are quite loud, and I can think of a fair few who can be a little piercing (peafowl, argus, etc). Also macaws, cockatoos, and penguins among others are pretty grating on the ears but remain popular in zoos (and private trade for the parrots at least).