Papers Please is a game about choices. Before you collect your jaw off the floor, it's also secretly about metagaming and metanarrative choices. The Inspector never really voices his opinion one way or the other about events in the game or the choices you have him make. If you have him follow regime directions to a T, perhaps he does so out of cowardice and a lack of will to do anything but try to get by. Perhaps he does this because he is actually an ultranationalist who genuinely believes in the Arstotzkan state.
If a player chooses not to engage with the game by inserting themselves into the empty vessel of The Inspector, but instead fill said vessel with a personality of its own, they radically change how the game's core ethical problems play out. From the perspective of an ultranationalist, a person with incorrect paperwork trying to enter the country to join their family is no longer a wicked problem, but simply a case of incorrect paperwork. No more ethically challenging than someone filling out the wrong paperwork at the DMV. Similarly, their relationship to Jorji changes radically as well. He is no longer an affable buffoon/drug dealer, but a common criminal who routinely tries to subvert the righteousness of not-Soviet socialism.
None of this is to say that the game is intended to be played in this way. Clearly the somewhat abstract pixel art (ignoring a host of technical or other artistic reasons) contrasts heavily with socialist realism and is instead meant to invoke the feeling of living in a gray, Soviet bloc country. Similarly the situations are set up to appeal to most people's sense of ethics, but they won't appeal to everyone's. Spend enough time on the internet and you'll come to realize that there are still diehard Soviet supporters around (and not just in ex-bloc countries) who would engage with Papers, Please in a radically different manner than most Westerners would. The metanarrative choices available to players of Papers, Please allow them to roleplay and inhabit radically different points of view, not just from their everyday lives, but from the expected emotional narrative of the game designers as well.
I think you raise some interesting points here, although I'll just address your first one — about how the actual in-game protagonist's character and sympathies are left mostly indeterminate. I think this anonymity may have symbolic intention behind it — the state worker as silenced being the most obvious reading. But I also think this silence could reflect on the way morality itself works — how much is your conclusion about the morality of a given choice based on your own private thoughts leading up to and after it, and how much is it based on the choice's external consequences (be they practical and quantifiable, like your wage, or social and qualitative, like the spiteful curses or desperate pleas by…
I definitely agree that the ability of a game to deliver interesting moral choices depends on the player's moral system. I often find situations where I think a choice offered in a game is stupid because one option is clearly more moral than the other. This is made worse because I'm really self-righteous and some of my convictions are unconventional. I think Papers, Please does a better job here than most games because many of the choices involve four or five competing values, not just two. This still isn't perfect; if a player thinks one of those values is more important than any of the others, like if they believe the authority of the government matters above all else, then…