I agree with you on this, and would add that swords where considered made for battle (and thus forbidden in cities) if they had 2 cutting edges, leading to people using falchions to "cut sausage". It great that Bannerlord added this feature in the game, it adds authenticity, even if it's a bit hard to know what's considered civilian and what's not (especially if you want to craft your own weapons).
Feels to me like it's loosely based on real-world customs, only it's sort of a mix of them from various regions. The only one I can talk in-depth about is the sword as it pertains to western Europe during the early stages of chivalry. "Swords", meaning true, arming swords or longswords, are not battlefield weapons (as opposed to greatswords, which are, but are a totally different sort of weapon compared to a sword you would wear on you hip). Arming and long-swords are sidearms; the closest, modern equivalent would be a pistol. In battle, you didn't want to be in position where you needed to draw your sword: that meant you had lost your "real" weapon. Swords are by and large useless against pretty much any type of armor. A spear is better at piercing it. An axe is better for dealing up-front damage and leaving grievous wounds. A mace or hammer is much better at just getting through it with concussive force. Any polearm or beaked weapon is best for hooking the enemy's armor or shield to knock them off balance and create openings. A sword's primary use on the battlefield would be defensive. It's light, well-balanced, and can be wielded with a pretty tremendous amount of skill. But the only thing it can really do against an armored opponent offensively is get into the chinks of the armor for a stab or a cut...and any knife or dagger is a far better tool for that if you're going to get in that close.
So...what's so special about a sword? Primarily, there's no more effective weapon one could hope for against
un-armored opponents. Against simple cloth, leather, or flesh, a sword is devastating. It can be wielded extremely fluently, and would create both an offensive and defensive advantage against pretty much any other type of weapon if one's opponent had no armor to back them up. It can be wielded far more quickly than any axe or cudgel. It can be used to directly close the distance on a spear or polearm. It can beat the reach of a knife or dagger. Without a ranged weapon, people facing a person weilding a sword are in dire straights unless they're also well-trained and have a sword of their own.
Hence, laws were passed that would prevent the average brown-bread-eater from walking around in society with a sword on their belt. Only people of prestige (initially, only nobles and knights) were permitted to own swords, let alone carry them. In a sense, I think it was a great deterrent. Just the sight of someone walking up to a troubled situation wearing a sword would set people on their heels. Similar to how a "display" of sidearms in the modern day may neutralize a situation without them actually being used. However, if anyone and everyone can have a sidearm on them...now it's more likely to escalate a situation and result in violence.
Thus, only weapons that were also considered "tools" were allowed in respectable society: knives, wood axes, crafting hammers, bows, a boar spear, etc. Weapons that were designed for warfare were outlawed: battle axes, warhammers, polearms like halberds or glaives, etc. And the sword was among the most paramount restrictions, as it was not only crazy-fast-and-deadly off the battlefield, it was also a badge of status and position.