I’m pretty sure Conan could use any weapon he could lay his hands on.
It’s the restrictions that are a bit silly and old fashioned.
Sure, but how much of the D&D Barbarian is actually Conan?
Conan's "rage" is almost nothing like how D&D rage is portrayed. It's basically just him being high on battle-induced hormones. Further, Conan wasn't illiterate, even if he wasn't
educated in the usual sense (having been enslaved as a child). D&D has done what it likes with the Barbarian class, without feeling beholden to Conan even as it draws inspiration from him.
Personally, I think we need to bring back Exotic weapons (the way 4e defined them), and do something like...
- Fighters are genuinely all masters of weapons, but Battle Master Fighters are especially so; if it's a physical weapon, a Fighter can wield it properly, and a Battle Master can wield it well
- Barbarians, Paladins, Rangers, and Warlords specialize in specific branches, but subclasses can tweak this as needed (e.g. a "Whirling Barbarian" might get access to Scimitars)
- Rogues, Assassins (if a separate class), and similar "martial but tricksy" classes get specialized weapon sets, e.g. a Ninja subclass of Assassin gets kusarigama
- Everyone else can truly only dabble in martial combat unless they multiclass or spend two feats (one for proficiency, one for mastery), e.g. Bladesinger Wizard gets only rapier and longsword proficiency, no specialization, nothing exotic, no mastery
That helps to reinforce weapon use as the distinctive
thing of primary-martial classes, and puts significant barriers in the way of a spellcaster trying to be as good in melee-related fields as an actual martial. E.g. it shouldn't be the case that a Bladesinger Wizard is a better "tank" than a defense-specialized Fighter.
From there, each martial class can be differentiated more by what they
do with their weapons. Maybe Barbarians mark their weapons with runes using an enemy's blood, or their own blood if they don't have any enemies on hand--magic effects which provide a passive benefit until the Barbarian crits, consuming the rune and adding a powerful extra. Maybe Paladins leave a searing brand on their foes, which
others can trigger, but the Paladin cannot--emphasizing their "inspiring others" element. Fighters know how to squeeze the most out of any weapon--perhaps they get
two mastery properties for any weapon they wield: the baseline one, and then a second from a Fighter-specific list, with each level letting them pick another "perfect mastery". Etc.
You get players to do things by giving them reasons to do it--by making the results rewarding, and making the process engaging. Seems to me that doing that with the Barbarian's weapons, rather than writing a bland blank-check for "wield whatever you want", is much more likely to make martial characters feel good to play
and make weapon choices feel interesting and rewarding.