The problem with that approach is kinda twofold. First, the problems you threw our way so far all were geared for violence; the feral ghouls, the group of proto-raiders. The beastie, too, basically screams "boss monster fight" to pretty much anyone; "acquire armor, acquire weapon, kick monsters' arse, grab spoils" is the conclusion pretty much anyone will draw, rather than trying to talk with the man-eating monster on the off chance that it might not find them as appetizing as it did the last bunch of humans it came across. That doesn't communicate "you need things other than violence to solve problems", it communicates "you need more capabilities for violence so you can survive with that sort of stuff around". Especially BECAUSE all of this is happening so early in the game; it creates the first impression that you're running a game with a Dark Souls esque level of difficulty, and players will react to that impression accordingly; emphasizing weapons, armor, ammo, and the like when scavenging, defenses like walls, traps and watchtowers when building, and so on. The end result is almost certainly going a near-constant escalation.
For another, it basically punishes us for having areas we're good in. Our character's good at fighting, so you're apparently throwing things that can't be out-fought at him. Presumably, this would also mean that being good at science means he'll face some sort of opposition that will be able to out-science him. If he was incredibly good at diplomacy, or at intrigue, the result would presumably be the same; opposition that is better than the character at his own specialties. There are two potential results from that. The first is, as I kinda indicated above already, that the players will attempt to escalate and raise stats/abilities further and further on the chosen area of specialization. The second is that the players catch on, and instead go and make sure that future characters will be jacks-of-all-trades at best, and completely inept at everything at worst.
Simply put, it creates far more problems than it solves, and is just as likely to have the opposite effect of what you intend. If you want to underline the need for the character to have administrative and social skills, then the solution is to throw problems at the character that require said abilities to solve for an optimal result. For example, when going out salvaging, the characters could encounter a group of other scavengers. With a violence-capable character the players could then simply go and shoot the scavengers and take their stuff, sure, but far better long-term results would be possible with diplomacy; convincing the scavengers to join the players' group, or making contact with another group of survivors for trade and mutual defense.
Or maybe a small number of people from our group want to leave, perhaps to search for relatives, or get away from the radioactive crater to someplace slightly less irradiated, or something else. Neither science nor combat would be able to really provide any sort of good solution, whereas diplomacy could help convince them to stay and continue helping out.
Something to keep in mind, though, is that our charter is not our civilization as a whole. He might not be rather mediocre at diplomacy, and utterly suck at intrigue, but Manny is pretty good at the latter, while he and Alessandra are both good at diplomacy. The MC and Alessa meanwhile are good at learning, which Manny's mediocre at, and have pretty good moral compasses, whereas Manny is more callous. And so on.
Considering the amount of adventure games I played, both in the past in general and recently, this sort of moon puzzle logic makes perfect sense to me. I approve!
