Barbarian magic suppression skills...

But when controlling Executioners, (due to the debuff), the initiative will decrease significantly...

Let it even drop to zero. The goal is achieved - the stack is taken out of the battle and loses Fury points. Two casts - two stacks. And it cannot be removed by absolutely anything. If Blind can at least be dispelled with a "kick in the butt," then Dominate simply cannot be. The same applies to Berserk. It cannot be removed or blocked. The only option is to put a berserk stack against either an insignificant unit or a very durable one (for example, Warlords, but they shouldn't take down the enraged ones in return).
And compare it, for example, with Anti-Chaos, when the damage of attack spells is reduced several times, and the Shield of Fury absorbs it. Is there a difference?