If they're just looking for something to say on the other end of the phone when you answer, isn't "Mr. Lastname" the appropriate thing to enter in that box?

No, it's not, because calling someones phone is also culturally dependent. Because in Germany, when you are calling someone, it is expected that person picking up the call will speak up first and introduce themself. Something like: "Herr Mustermann, hallo!".

You see, if you are calling person from Germany, knowing how to address him is not enough, you shall still know how to make a call. If you don't know that, you'll be rude anyways, and if you know that, you'll also know a proper way of addressing persons in different cultures.

"When a recruiter or employer contacts you, how would you like to be addressed?"

Is there really any further scope that should be covered? If there are specific cultural issues, shouldn't that be hammered out later?

Really, the design question for JSON Resume is "For what purpose is a name being provided?"