To my mind, there is nothing particularly special about the questions you're asking above with respect to Hardholder. In my recent Dark Sun game (which was more of a stealth sandbox than an overt one, to be fair, but was certainly a fairly trad game, being run with Mythras) I was very interested to see how the PCs would react to learning that all was not what it seems in the village of escaped slaves where they found refuge. Very specifically relevant to your examples, how they would handle water sources that they need but so do other perfectly decent people. How they would balance pragmatic needs with offering people basic human dignity. Seeing how characters deal with moral quandaries and conflicting priorities has always been part-and-parcel of my gaming, sandbox or not, and I am surprised to see anyone suggesting this is rare or unusual.
OK, my list of questions about the Hardholder was a pretty superficial description in the sense that it didn't delve into the rest of the process and how it all hangs together: The player chose to use the hardholder playbook, a playbook which specifically casts the character as at least an organizer, if not outright leader of a community or group, the inhabitants of the hardhold, a refuge in the chaos of Apocalypse World. The hardholder player will describe this place to at least some extent, and the rest will be discovered in play.
In your example of Dark Sun and a village, etc. you chose to create a village, and give it some circumstances which YOU were interested in. Do you see the difference right off here?
Now, it may well be that the GM, at some point, makes a move, or reveals a threat, or a clock tick brings a threat to enact some problem for the hardhold, lack of water in my example. This is putting pressure on the character because, presumably, they care about their community, or at least some parts of it. In your example, you also create a threat, but it isn't against anything that the players seem to have chosen to value. Instead presumably they will do something most likely because it is in their interests. D&D certainly doesn't foreground any kind of character motives or interests.
But notice the nature of my questions, they weren't just simple questions, they were also escalating, and focusing on the character. I was imagining this whole process. The PC is doing whatever, she's probably engaged in other conflicts, keeping the peace maybe, gathering supplies, whatever she does. Water is presented as an issue, in order to threaten the holding. First the player has to decide, will the character take the water needed by others? Maybe, maybe not. This is likely to bring some other conflicts too, the Angel may not be cool with taking the Sand People's water. Maybe it will turn the population against her! In any case, tough decisions will be made.
But AW is a game where things escalate. The world isn't OK. Maybe she decides to share the water and now some people are pissed and she's got to decide, will I bust heads? Will I resort to violence? Finally, the situation gets crazy, the character's sister somehow gets involved, will she kill her, or whatever the situation is? Play to find out.
It is a very different kind of structure of play. As I said in the first post, I have never seen trad play do this. I have seen some dramatic trad play, but it was always more focused on something the GM planned out, like your village, with a plot attached to it.
