[lmm]

One good use case I can see is where you want to add convenience "helper" methods to an interface that can reasonably have default implementations in terms of some other method on the interface (E.g. overloads to emulate default parameters). Or for methods that can be implemented in terms of another method, but might have a more performant direct implementation (e.g. Collection#get can be defined in terms of iteration).

I don't quite understand your point about instance variables. Instance variables are and should be encapsulated. An object that implements multiple interfaces must of course provide the correct semantics for all of them. But that's true whether an interface contains method implementations or not.