Elise is an ap jungler and not a tank
Tank is an archetype, AP is not.
You're comparing apples to the color green with this.
Just because Elise fits one doesn't exclude her form doing the other, and having AP scaling doesn't mean you should go glass-cannon.
Also - Elise is largely a fighter, getting a mix of both AP and defensive items.
And she very much has a fighters kit.
If you look at fighters, the common trend is they get amazing damage through bases, and a lot of mixed damage that's difficult to counter-build: a combination of physical, magical, auto-attack, and ability damage. Often with %HP, True, or armor/mpen steroids thrown in the mix.
This lets them build defense without having to worry about a squishy hard-countering them with 1 item, and it also makes building full-damage offer less scaling, really pushing the bruiser-build path as the optimal one.
And look at Elise - she has a 120% attack speed steroid with 40 on-hit magic damage and another 40*5 = 200 magic-damage from 5 spiderlings, along with 2 8% current and 8% missing HP skills, along with a melee form.
She's very much designed to want to endure so she can unleash a lot of her magical auto mixed-damage.
Its no fun to build her bruiser/tank as the old crappy Elise.:)
Bruiser Elise was only crappy because Riot nerffed Elise. Bruiser Elise was very solid when Elise was solid, because Bruiser has always been her optimal build path.