Annie does not have the range of Syndra or the in-combat Mobility/Zone Control of Taliyah. And, for the most part, Annie's E eats out her power budget. If she didn't have her Defensive E (we know sure as hell Riot isn't giving her a dash), than she's going to get more damage because her thing is "Burst Mage". (Liss can ult herself for a reason, it's an ult that can be used defensively or offensively as the situation presents. Don't make it binary)
And yeah, it does make sense. She is a very low range mage, whose entire shtick is to have a single period of Burst to take out her target, and then she kinda hopes she doesn't die afterwards. Her E is a part of that "This time is my kill time" since it's only 3 seconds long, and if she's in range of you, YOU are in range of her. If she didn't have a defense buff, than she needs more damage, as it becomes a contest of "Did I survive your burst? (No) => I'm dead. (Yes) Well, you're dead." which is extremely binary, and the thing Riot tries to shy away from.
It's the exact same reason why Riot gave Talon his over-wall Mobility, or Leblanc her Clone from Ult (the one that appears from anywhere). They're things that AREN'T damage to help eat up power budget, while increasing a Characters power, without adding damage. Annie lost A LOT of damage from her Kill pattern. Early game, it is impossible to 100-0 easily because of it, and late game, if she wants to get in range of other people for her Kill Combo, it requires her getting that close in the first place (withholding Flash, because everyone can have flash for their kill pattern)
PENE EFFECTS EVERYONE. It doesn't matter who, it doesn't matter what, if you're building defense or gaining it naturally, Pen is meant to counter that. It doesn't matter if you're Jax, a Tank, or a mage with Zhonyas, Pen is meant to make anyone with resistances easier to kill, it doesn't matter if you're a HyperCarry or not. They don't get a special exemption from the rule, Pen is meant to make anyone who has resistances easier to kill.
And you're telling me, Jax can't fight a Tank when? Early game when Jax is weak? Mid game when Tanks are strongest? Or Late game when Jax is strongest? Because I'm honestly calling bullshit there. And what if, just maybe, Jax's intended targets to kill aren't tanks, and is weak against them on purpose? Maybe he's meant to get in the backline quick to start poling carries up the ass?
And for a final comparison, let's look at other Mage's defensive measures. Syndra has a huge knockback with a 1.5 stun added if Ball'd, and can cast abilities while moving. She also has more range than Annie. Cassiopeia can deny enemy mobility, gains speed with Q, and can Stun for 2 seconds. Her main damage (E) is low range, but still a higher range than Annie. Ahri has three dashes, a charm and speed boost, with semi-low range, but more than Annie. Annie has damage and a single 1.75 stun, well having literally the lowest range of any mage in the game. Either she get's a defense ability, or she gets more damage and starts insta-gibbing with no counterplay again.
Annie has her buff for her own reasons, and Jax has his for his reasons, each reason different by how they are played, and the aspects of them. Does Jax need a buff? Yes. Does comparing Molten Core to Jax's Ult (Which still has actual damage to it) as a reason for a buff a good one? No.