Closures capture variables so have significant differences compared to inner functions. Capture can affect lifetimes so the difference is significant in Rust.
Perhaps it's due to the fact that you can't really have type-generic closures in Rust: once the compiler has inferred one type, the closure cannot be used with another type. In contrast, inner functions can have any number of additional type parameters.
module functions: if I chose, I'd let them be derived, but I'm relatively indifferent
inner functions: should be allowed to be derived, IMO. They're very infrequently used so this choice doesn't have much impact.