It's thematic, gives her magic damage on auto and innate spellvamp, and synergies will with her signature item - the gunblade. Nowadays the gunblade heals you for all damage dealt, so all of her damaging spells and her passive damage plus spellblade proc from lichbane if you have them count towards her healing.
Her passive is a core part of her identity, and is a large part of what allows to survive in lane pre-6.
And no, the difficult to balance part of akali isn't her passive, it's her ultimate and q combo. It creates a situation where getting caught out of position by akali means there is no running away and no juking her damage - she WILL catch you every time and she WILL land her damage combo on you.. so it comes down to whether or not she has the damage to kill you or not without much that any squishy champion can do other than try to kill her first. THAT is the volatile, hard to balance part.
If you weaken her damage or chasing ability by slightly too much she become unable to ever kill anyone and just dies because her attack pattern requires 2-3 damage rotations to kill a single target unless super super fed, unlike other assassins like leblanc who can just pop in kill instantly and run away. But if you buff her damage or chasing by slightly too much she will always catch everyone and kill them without them being able to stop her.
They did nerf her ult range not too long ago and right now I'd say she's doing better than previously because sweepers don't reveal stealth anymore so literally everyone can't just buy an anti akali shroud button for cheap like in previous seasons if she gets ahead. But twin shadows still exists and so do cheap pink wards, so it's not like her stealth is perfect either.