Nunu, Amumu, Hecarim, Rammus, Skarner.
There is really no "snowballing" required here, they just need to remain tanky enough to be unkillable, and perma gank (soaking lane XP).
Getting their laner ahead means my squishy jungler cannot _touch_ them, I am de facto 2 levels behind solo laners and will just pop.
Jungle is so unforgiving and nobody wants to play it. I swap with somebody who's autofilled because they say they're terrible. Guess what? I go 0-5 against Nunu jungle and the ADC is flaming me.
Unless you are playing a spam gank jungler there is no point in the role. The game will be decided by 20 min because the enemy jungle perma ganked.
Laners can easily AFK farm until 10-15 min to get their great item. But junglers have to waste 10 minutes getting their "special jungle item" that has basically no synergy with their kit. And in that time they must perma gank if they don't want to turn into a super minion.
With the abysmally low jungle XP the only junglers that can actually gank without exploding are tankier ones. Thus we end up with these stupid "movement speed tanks" like Nunu and Hecarim that tilt the heck out of me.