Could also be that Klingon muscles are different from ours, they have a whole bunch of redundant organs after all, and the Batleth is designed to take advantage of their unique strengths
Physics does not work that way, you insolent fool!
Regardless of Klingon muscles, the fact that the blade sticks out sideways from the handle creates a lever arm that tends to make it droop due to gravity whenever it's held horizontally. Even if Klingon hands are different, they're not that different that it's somehow advantageous to keep torquing upwards so the blade points at the opponent instead of the floor.
Yeah it often is described by Klingons as a monastic weapon, meant to teach a lesson or discipline while training with it. I don't think the idea is for like a formation of Klingons to march into battle all wielding Bat'leths.
You train with a Bat'leth and then when a real battle comes you are more prepared to fight with other weapons, or even unarmed. It even makes sense in that the Bat'leth is a very complex object. I can totally see how simply trying to spar with it would force you to think more about all the different ways you can use the thing in your hands to your advantage.
I thought that was cannon? It's that not specifically mentioned somewhere? I can't remember when I heard it but I always thought that they were made to be hard to use, because winning a battle with a regular weapon is easy and therefore less honorable.
And if you watch the actors try to swing these things around they always look awkward.
Even worf seems to agree, by Picard s3 he has a sort of batleth / katana hybrid instead of a classic one. Though I think he already said in DS9 that he actually prefers the mekleth.
It’s a Mek’leth (modified in PIC S03), which he has stated before is his preferred weapon. He even uses it in The First Battle of Deep Space Nine to defend against the attempted Klingon invasion.
Like, it's a fake weapon, badly designed, intended to look cool. But in universe, what's the history?
There's multiple ways to give a canon reason a badly designed weapon is such a cultural icon. Maybe it's based on the horns of a predator, or something like that, as an example.
I'm not a deep delver into such things, but I wonder if there's an official history behind it.
Like you guessed it is a cultural icon. The emperor that united their home world used it.
In Star Trek lore, the Klingon Kahless created the bat'leth around CE 625. According to Klingon mythology, he formed the blade by dropping a length of his hair into some lava from inside the Kri'stak Volcano, then cooling, shaping, and hardening it in the lake of Lursor.[5] He then united Qo'noS, the Klingon homeworld, by killing a tyrant named Molor with the weapon, which became known as the Sword of Kahless.
See, that makes sense why it's a less than ideal design. We have weird weapons here on earth that have significance, but aren't ideal designs. The batleth is more of a hungamunga than a longsword :)