I take issue with the premise presented: that heals are unique to leaders and so on. Paladins are defenders that can heal as a Daily Power. Nor are marks unique to defenders. Clerics can mark as an Encounter Power.

What makes leaders “own” healing or defenders “own” marking is that they can do it consistently and reliably.

So then controllers do have their own domain of things they do reliably that other classes can only do intermittently: AoEs and status effects (slow, daze, etc).

Example off the top of my head: the Wizard level one At Will Powers.

Cloud of Daggers
A zone of denial. Enemy takes damage if they pass through.
Magic Missile
Wizard basic ranged attack. Unremarkable for this analysis.
Ray of Frost
If it hits, it slows. Every time, every round.
Scorching Burst
Ranged Area of Effect. Puts the hurting on any 3×3 square.
Close Area of Effect. Puts the hurt on and pushes away.

This is the essence of the controller. Other classes have an AoE or two, maybe as an encounter or daily. Other classes have a slow or two, maybe as an encounter or daily. But controllers can be relied upon to provide this stuff at will.

That is their (in the words of the original poster) “unique” mechanic.