But aren't asymmetries, arbitrary as they may seem, more interesting and believable than perfect symmetry? Symmetry always feels formulaic to me, while asymmetry feels more natural.
In a game world built around factions, you HAVE to have symmetry in order to achieve a proper agonistic choice when the player has to take a stance.
Plus in a system where everything makes sense because it is authored (even procedural worlds derive from a seed, i.e. a kernel of "sense"), asymmetry is an illusion (a crafted one that gives the impression of a living, breathing world when properly done, but an illusion nonetheless).
What feels contrived however is when you only have binary options, that forces the player's hand into going into one extreme or the other. Usually introducing a third option is enough to break this abusive symmetry, be it a moral one (good vs evil), a functional one (resolving a quest by sneaking vs combat), or one that spans worldbuilding as a whole (Legion vs NCR for example). In all those cases a third option introduces some salutary wiggle-room for the player, but also by breaking the binary logic enables us to choose, mix and match approaches, instead of emphasizing two other-end-the-spectrum elements.
See, the kind of symmetry that I find formulaic and that was kinda expressed in Infinitron's post by the way he phrased it (some of PoE's companions are not permanent but die, why? This one faction in NV has no companion NPC, why?) is the symmetry of handling each faction or gameplay option in the same way, following the same formula, making it appear inorganic and forced rather than like a choice that grew from the world and story of the game.
Example: there are four factions in the game, each faction has one follower NPC you can recruit, each faction has a headquarters, each faction has you do 5 quests within their faction questline, each faction questline starts with you joining them at a low rank and ends up with you attaining a high rank.
That often ends up making the factions feel formulaic, samey, and gamey, because mechanically they are the same, even if the content differs.
Changing up the formula and making one faction play differently from the other, or offer a different experience, is the kind of asymmetry that not only makes the game world feel more natural but also lends more significance to player choice. One faction might offer more content of one type, for example, while another might offer none of that but more of another.
While Caesar's Legion was overall a little underdeveloped in NV, let's take the example of "there is no companion NPC for the legion" that Infinitron mentioned. So, every other faction has one or more companion NPCs, but this faction doesn't. What if, instead of adding a companion to create symmetry, you add different types of content to make up for the lack of a companion? This way, the faction would have one clear difference from all the others, and it could even be reflected in its overall gameplay and style. Maybe it's a faction that expresses the "lone wolf" approach, and that is an in-world reason for why it doesn't offer you a companion NPC. Maybe the faction offers you more infiltration-focused quests, or maybe a generic "bring us intel from other factions and we reward you" thing that the other factions don't have.
And boom, you got yourself asymmetric and interesting factions that actually play differently and offer different types of content to the player.
Same with approaches to gameplay: if you have a combat, stealth, and diplomacy approach for your encounters and quests, you should strive to allow for each solution in the majority of quests. As in, 90% of quests allow for one of those three options to be solved.
But then, you also have 10% of quests which can only be solved one way, or only solved two ways, instead of allowing for all three approaches. Some players will then likely fail those quests because their character isn't built for braving that kind of challenge. Sneak into a nobleman's mansion and steal blackmail materials on him without being seen? Well, looks like combat and dialogue focused chars won't be able to tackle that quest.
And that is some much-needed asymmetry that makes the game feel more realistic and believable, more natural, less perfectly arranged: it is only realistic that most characters won't be able to solve every single quest in the game, and that there are some tasks that just don't fit into their skillset but would be perfect for another character. It breaks the formula and therefore makes the game feel more varied and alive.