Why are things like Statikk Shiv still designed as melee weapons despite the expectation they will be used primarily by ranged champions?
I'm pretty sure it's mostly about symbolism.
First, Play just about any vaguely medieval game and "damage" is represented by a little sword in well over half of them.
Second, the base items in LoL are the same base items the game started with. If the base item components for damage are swords and daggers, a lot of items built from them will probably be swords and daggers.
Third, silhouettes are pretty important for ease of recognition. Different builds can mean vastly different things in-game, so it's nice to be able to press O and easily see a champion is going AD adventures by grabbing a lot of swords. Also nice to see a champion going tank with a lot of shirts.
Having a solid mix of halberds, whips, nunchucks, crossbows, morgensterns, pants, helmets, and musical instrument icons is nice for ease of recognition between the different items of a given category, but just using color is much more efficient and even easier to differentiate differences with, so sticking with swords gives shape and color advantages - where with things like morgensterns you could have very similar silhouettes to star-shaped medallions and spiky armor, making it harder to discern between damage and offense builds on the flay.
Probably also the reason there aren't any pants in LoL.