One of the organizational problems I've seen with ENVs are when there are too many of them. When someone starts up a new environment for staging or production, they just copy all the ENVs from another environment and don't bother going through each one to see if it is valid or safe to copy. So you end up with a testing environment that can send real money. What fun! Been there!
This can happen with configuration in code too but at least it gets checked in and there is usually a better review process.
So I usually go for a hybrid approach. Have most configurations committed and tracked in code in different files, one for development, production, etc. This makes it really clear which configurations are more important. Any configurations that can't be committed to code, use ENVs or a secure key store if you can handle the extra process complexity.
This approach can still have holes but at least the surface area is reduced.