My definition of a health assassin
So I've been maining Akali for a while now and I can honestly say without a doubt she is one of the more healthy assassins currently in the game
What is an assassin to me? An assassin to me is someone with high burst potential, great outplay potential, high reward, high risk, low skill floor, high skill ceiling,
Now Akali does meet a lot of these requirements, she has very good burst potential with her full combo, if she gets off 3 q's 3 e's and 3 r's her full combo's base damage is 1920, + 540% AP + 180% AD, now this may seem extremely potent and high, but it does take a decent amount of time to get off 3 full rotations.
This factor adds to the high risk when she's going in on a teamfight. She has great outplay potential in the form of her ult, and that's pretty much it for that, it's not a Zed W or R where she can simply blink back to safety, or LB W for that matter so it doesn't make the ability too OP.
She scales extremely well into late game and can usually do a lot with a couple kills which compliments her high reward. If she goes into a teamfight too early or gets CC'd by a tank that contributes to the high risk, I mean we can say she's not high risk all you want, but at the end of the day she has the highest risk of going in a teamfight than any other assassin out there, since her mobility is attached to hostile targets only.
She has a low skill floor so she's easy to pick up and play, but a high skill ceiling where if you really want to learn the ins and outs of her kit, learn when to go in and how much dmg etc you can do, it requires some mastering.
Zed's ult and W cast are considered a blink when they are already out so it's hard to counter something with no projectile speed, Kassadin can flash every 1.6 seconds, LeBlanc's W has a pretty fast projectile speed and the return is considered a blink, so once again hard to counter something with no projectile speed, so all these champions can be in and out within a second of completing their combo, Akali cannot as her mobility is not ground targeted or a relocation, (
Fun fact Akali's R has a 1 second cooldown at rank 3 which means it takes the same amount of time for it to come off CD as it does for Zed to get off his full combo and blink out, Shadow Dance (R) can also be intercepted by CC such as Gragas body slam, Sejuani charge, and every other form of CC. Tell me there is no counterplay to it..
[Edit] Thank you @DanofDemacia for this section of the edit "She is the only assassin that actually has a bad laning phase. Every other assassin can stay safe somehow. Akali cant." With the removal of Akali's E proc it's a lot harder to effectively proc Mark of the Assassin, making her laning phase even more sh*t that it use to be, and that's another thing assassins should have, a bad laning phase to make up for the potential snowball later on.
TL;DR Akali while being a point and click Assassin is probably one of the most balanced assassins currently out there at the moment.

At least Akali is visible when dealing damage, and doesn't have an instant escape. As a jungler, I prefer having an Akali on the enemy team rather than those two. Lot easier to kill an Akali.