The main difference is that functional package management lets you declare the system state. Free rollbacks are a consequence of being able to fully describe the system state.

With a file system the storage pool is dumb and all meaning of higher-order abstractions (such as packages) is lost.

You don't use functional package management just for deduplication, but in order to be able to declare and reason about state.

(I work on Guix, which is an implementation of functional package management, but with different abstractions.)