If they are your pets, or you keep a backyard flock, then there is no need to kill them!
Yes they will remain carriers, but they will also be resistant to getting that disease again.
Since that disease is in your area, if you culled you birds, and got new ones.......the new ones would probably get they disease too.
Now you birds will have immunity and you won't have to worry about then getting that illness again.
People who show the birds must, of course, take the responsibility not to spread diseases about to other people chickens.
Actually, all my chickens recovered from infections bronchitis and I have even added new chickens and they never caught it. I did source my chickens from neighbours and local area, so probably they have resistance to diseases in my area.
All the chicks that hatched from my hens are all healthy too.
I am sometimes confused about the attitude people have with their birds. If they were dogs, cats parrots people would not be so quick to cull them if they are ill. I do understand the need to cull chickens if people are farming them or using them as a business.