What I like about Java functional interfaces is that they give a place to specify an interface contract. For example, with Comparator, it specifies that instances must implement a total ordering. Purely structural function types don't have that affordance.

A slightly problematic point, however, is that you can assign a method reference from one functional interface to a variable of another functional interface based purely on structural typing, even if they happen to have incompatible interface contracts. For example, if you had a PartialOrder functional interface with the same parameter/return types as Comparator, then you could assign PartialOrder::compare to a Comparator variable although the semantics aren't compatible. Whereas nominal typing prevents you from assigning a PartialOrder to Comparator (no "duck typing"), Java circumvents the nominal type system here for method references, with the result that one may assign incompatible implementations without noticing.