Leblanc is supposed to be a deceitful trickster. I don't think a champion should be strictly balanced around a character identity, but it can still offer some insight into how she was made and, if she should be changed, a nice direction for her to take.
Her passive is a really cool mechanic that follows that theme. When her passive pops, it's a mind game between the Leblanc player and her opponents, and (as someone who doesn't play her) I really enjoy being on the opposing side of that situation. When I'm outplayed I feel a sense of admiration, and when I follow up correctly to finish her off I feel a sense of satisfaction.
Distortion, her W, has an element of that: the ability to blink back to where she cast it. There's a mind game going on here, too: predicting what Leblanc will do and trying to plan accordingly. However, my impression of her kit is that she doesn't need to rely on that mental game nearly as much as she should. The combination of such a long dash and lengthy option to blink back in a single spell (not to mention some healthy damage) means that she is reliably more mobile than almost every other midlaner pre-6. Post-6 she can repeat her dash/blink if she feels like it.
Mental games are fun (and create good game play) because they force both players to think several moves in advance. It's a battle of wits to accompany the mechanical skills of each player. However, when Leblanc's mobility is so overloaded, you can think purely reactively instead of thoughtfully and still prosper. Bjerg was quoted some time ago saying that Leblanc was a good pick because she was very "safe." I think he's touching on something close to what I'm talking about. If you want to use your high damage combo, the blink back ensures that you aren't sticking your neck out that far. That notwithstanding, you have a long range slow/root and, post-6, your dash gets twice as big. None of these things necessitate a deceitful mental game between Leblanc and her opponent to produce that insane damage that inspired the OP to post. Of course, if you're pretty good with her kit, when you do think a few moves in advance, things like this happen:
https://www.youtube.com/watch?v=JDd3diN37pU&feature=youtu.be
(was featured on big play spotlight some time ago)
Don't get me wrong, this was an impressive play. When I saw it I thought "Wow, they're really good." I also thought "...should a champion be able to do that?" (I also have some opinions about thresh, who also made that play possible, but this isn't the time or place.)
So what's the problem, and what can be done about it? And what the hell does Goose know about anything, anyway? (A lot, nothing, and not very much?)
Here's my two cents, and hopefully it furthers the discussion:
I think OP is right in that part of the issue is the damage. I don't want to play mental games with Leblanc early (or, if she does well in lane, at very many stages of the game at all) because if I lose the game the penalty is really, really harsh. Apparently, at level 2, it's the second harshest in the game. Considering how easy it is to land compared to the harshest, that's a pretty raw deal for Leblanc's opponent. However, I think a ham-handed reduction of her damage would be a pretty lousy solution because it doesn't address any of the other issues discussed above. Reducing ranges could make things a bit more forgiving for opponents and some matchups (disregarding that Leblanc does well against skillshots), but is a similarly flawed solution. It's also what happened to Akali, who has since statistically plummeted into obscurity.
I think the mechanics of her Distortion should be augmented to allow for more counterplay and encourage more deception and mind games. Chimera hit the nail on the head when he said that her Distortion is difficult to punish. Right now there's very little incentive for Leblanc not to blink back to the cast point. Giving some incentive or trade-off could make the ability more interesting and forgiving to play against... Reduction in movement speed or similar debuff if she returns, reducing cooldown if she chooses not to return, an additional mana cost for returning, etc. Or making it simply more difficult to return, such as a minimum time limit Chimera suggested, or making the return also a dash instead of a blink. I'm sure there's better and more creative solutions than I've come up with off the top of my head.
was nerfed because his early game was obnoxiously overpowered?
What about 
? She's banned in China and other regions because of how safe, bursty, and extremely mobile she is. I'm big on counter play and when I lane against her, I usually displace her W to prevent damage, but she can still pop her Q with E and deal tons of damage while rooting me. It's bullshit.
level 2 base damage
Plasma fission: 80
Void rift: 30/45
Deconstruction: 45
Total: 200 (phew vel'koz OP)
level 2 base damage
Razor shuriken: 75
Mimicked shuriken: 37.5
Total: 112.5
level 2 base damage
Ice share: 75
Ring of frost: 70
Total: 145
level 2 base damage
Arcanopulse: 80
Empowered W: 90
Total: 170
level 2 base damage
Dredge Line: 60
Riptide: 120
Staggering Blow: 14 (1 AA is pretty much guaranteed after Dredge Line, but since you ignored the actual AA damage so will I)
Total: 194
