I guess my comment seemed answery & I used to have such fond memories of Bleach so here goes. Disclaimer: if you're willing to accept lazy filler writing as the answer, do not read anything below this statement because I don't have classes tomorrow so I thought I'd write & reminisce.
Reasons why the personification of Zanpakuto do not directly reflect their shinigami
Literary sense would dictate the following:
- Character Overlap is unpopular & otherwise bad. You don't want to give every character of focus a clone. It's just bad writing to introduce partners as complete doppelgangers. It's different when that clone-character is referential to someone else (everyone in Naruto who was like Naruto) or substituting (also in Naruto, when Sai was a new Sasuke). Those are typically OK (but should not abused, Naruto).
- Lack of material is the biggest reason for every problem Bleach has ever faced -- this is fact. Otherwise, it'd still be a beloved powerhouse than a retiring flagship of entertainment. With identical plots, new characters or focusing on B characters seem like an OK idea to seem fresh.
- Filler arcs demaaaand disposable conflict, that is, sometimes you get ones knowing they're just buying time so they don't even attempt to seem exciting and other times you get game-changers and you cry knowing the cute girl who isn't useless will die or leave. In this case, everything would wrap up with a smirk by the sunset for "even though we had our differences, we'll move forward". Keep in mind, delivering this can be cheesy so it often gets rushed.
- Thought-provoking topics or questions like yours is a subplot waiting to boil but all too often it's just left to fizzle without details. Which leads me to my next speculated point,
- Self-reflection/acceptance implies dealing with the parts of yourself that you know you need and how to achieve them. Like, Ichigo's inner world reacts to the good (hometown, maybe more) and bad (raining on all of that, drowning in it) in his life. But his frustrations with himself turned into a seasoned old guy and animal instinct-man who create a demand that Ichigo needs to be stronger to overcome the odds. Rukia, the cute tomboy/soldier focused a lot on being militant, but has inner fascination with beauty only seen in her inspiration from Shiba Miyako (Kaien's wife), Byakuya's art & strength, and it can be argued that this is represented in her zanpakuto's embodiment. Also Sode no Shirayuki in this arc is bothered that Rukia's primary personality makes her just a military tool. Even though Muramasa's powers promotes the feelings of being oppressed to persuade the spirits to fight their Shinigami, the underlying ideas are still there in most of them -- or just secretly made up reasons to move plot because filler rarely has decent direction.
It's just a lot of open-ended conjecture that has good intentions of making fans expand on the characters they enjoy, hence those two examples up top and this following final piece.
Kazeshini's personality is one that Hisagi detests not solely because of how he is but instead who he is -- the extension of his very soul. He doesn't emphasize with Kazeshini which makes it a part of himself he cannot identify. Kazeshini reflects this confusion which is why they agree to disagree. Alternatively, if they meet halfway, neither would be stifled by fear (to kill) or frustration (that seems weak). Achieving Bankai is probably about releasing insecurities & inhibitions to become whole or enlightened -- you know, growing with your sword instead of against/away from it -- or that was the original idea.