In solo queue, there's really no reason to pick her unless you're already particularly good with her.
However, in team play...
For a while, immediately after it was released, Cinderhulk became the de facto jungle item. If you didn't build it, you were going to be trash and get trashed, even as a Warrior jungler like Vi or Lee Sin. It offered insane tankiness that scaled heavily into the late game, and a ton of damage just for sitting on your ass in the middle of the enemy team.
Then the damage got nerfed. It did significantly less to champions. However, it remained the top jungle item because of its huge scaling health bonuses. Warrior and Magus junglers were still shoved out of the LCS meta, because most of them didn't have the tools to deal with the tanks.
Tanks were still allowed to roam free, with no repercussions whatsoever. They could even run around in the enemy jungle, ward and travel where they wanted, and get out more or less unscathed, because the ramping damage combined with that massive health spike made them indestructible.
This is where Evelynn comes in.
She's virtually untrackable. Unless she's already shown up on the map, you have no idea where she is, and as soon as she leaves the map, she can show up anywhere else at any time.
It's a waste of money and wards to keep tabs on her. Everybody gets pink wards, delaying their power spikes, and jungler/support wards have to be put deep in Evelynn's jungle, which is an inherent risk in itself in team play.
Most importantly, she has the tools to deal with tanks. With sustained mixed damage, an anti-slow, and AoE %HP damage, she can both avoid and shred tanks and squishies alike as necessary.