So... Skill proficiencies may SEEM less valuable than combat proficiencies, but skill proficiencies can lead to an easier time doing a quest or allow you to avoid a boss fight. Also, the only classes that benefit from Civil Militia are Sorcerer and Wizard. That's just... Kinda bad.
Skill profs ARE less valuable than combat profs if for no other reason than opportunity cost. The amount of mileage you get out of something as simple as shield proficiency (+2AC) is infinitely more valuable than what you'd get out of ANY skill prof, the only exception maybe being persuasion and only because of the sheer amount of checks you can make. You can make all skill checks and saves without proficiency but you cannot use, or use with penalties, any item that you do not have proficiency in. Even the dumbest barbarian can make INT saves and checks, but the smartest wizard cannot use armor or shields without first knowing how.
If that's not good enough, the raw cost alone for combat profs is 4-8 levels and 1-2 feats, depending on what you take. You'd be paying through the nose for what two races give FOR FREE at creation.
If you really want to nitpick classes, Bard, Rogue, Sorcerer, Warlock, and Wizard can all benefit from Civil Militia, and since 5e has deigned that quarterstaves are versatile, you are actively debuffing yourself by not using shields on casters. On a flat d20, 2AC will account for about ~10% chance to hit, meaning with no hit modifiers, a no-armor caster with a shield gets a 40% chance to be hit vs 50% flat. Once hit modifiers start getting added, that 2AC will start flexing a lot more. Throw DEX and progressively improving armor into the mix, and you'll start seeing just how far something like Civil Militia will take you vs. that Nature proficiency you want to take in its place when the last time you even rolled Nature was 50 hours ago and failed anyway.
You have a fundamental misunderstanding of the importance of AC and what skill profs actually do for you. Rolling persuasion to avoid a boss fight is a unique option offered
at that specific time by Larian and cannot be used in any boss fight. However, +2AC can be used wherever you want. Its applicability is nearly boundless and outperforms every skill check you can make.