Comment by tsimionescu

The main idea behind culling is to prevent the virus itself from evolving inside the herd. Viruses evolve much more rapidly than birds.

Now sure, if there were a clear way to tell that some birds have been infected and survived and recovered, it could be a good idea not to sacrifice those birds, and even to specifically breed them. However, there is no good way to do so, especially not with any confidence. It's much more likely you'll end up infecting any population that you put these new birds in to.

So, the best and cheapest solution is to sacrifice the entire group, to prevent the disease from spreading to other populations, and to do so quickly, to prevent the virus from evolving or crossing a species boundary.