I cannot believe how many times I have seen a PROD (or new env X) deployment go bad from configuration issues. At least they separate configuration deployments from code deployments, that's a good sign. Why not take it a step further and instead of doing config deployments, use a config server?
In the end, you would still have config deployments, but to the config server. And if you can push config to nodes needing it. you have one less point-of-failure, right? I'm not too familiar with the concept of a config server.