First of all, don't tell me about how it doesn't make sense because interfaces don't have private data. Yes, that IS why you can't right-click on an interface and select "VI for data member access" like you can on a class.
HOWEVER, on a class, you can also create properties manually by selecting New -> Property definition folder, and then create the accessors manually by selecting "New -> VI from Dynamic Dispatch Template". In this way, you can create properties that are not simply the getting and setting of a member of the private data cluster.
WHY can you not do this on an interface?
And here's the kicker: if you create a normal virtual folder on the interface, save that, and then edit the .lvclass file in a simple text editor, you can change the type of the folder from "Folder" to "Property Definition" and EVERYTHING WORKS! You can then create the dynamic dispatch accessors and they become overrideable in child classes, and are still properties you can use in property nodes and so on!
So, there appears to be no reason for this limitation. The option was just removed from the context menu -- even though all the plumbing is there and everything works. WHY?
It's just basic object orientation. Suppose you have am interface like "Vehicle". You might derive child classes like "Bicycle", "Automobile", "Airplane", etc. Then, you define some properties on "Vehicle" like "Color", "NumberOfWheels". "PropulsionType", etc. These become properties the child classes must override, and each child class might obtain its value from a different source. There's nothing new or OO-breaking about any of this, and apparently NI has thought about this because IT WORKS if you edit the .lvclass file as described above.
