You aren't opening with HS -> Maim -> Eye with no offensive buffs. You will get the boss pulled off you in seconds.

So, acknowledging that, you're now starting with Butcher's. Unbuffed by Maim, or SE. Your OT is also losing damage because of this. So 6 GCDs where Eye won't even be up, all nerfed by Defiance's damage penalty, on top of the 6 GCDs your OT isn't getting buffed by SE in his opener (where his offensive buffs are actually being used).

With Unchained, you are no longer suffering the penalty of Defiance and can put up SE first, as well as gain Maim, and not be inflicted with Defiance's -25% damage penalty.

Also by gaining massive enmity in your opener, you are more free to alternate between SE -> SP in Deliverance or Defiance. While SE -> BB is more potency, as MT (especially in Deliverance) keeping up SP is extremely important.

Here is a triple FC opener that still uses Unchained, btw:

Infuriate -> RI @ 1s -> pull @ 15-10s -> Unchained -> OP/Tomahawk -> HS -> Maim -> SE -> [Brutal Swing] -> HS -> SS -> [Pot] -> BB -> [Deliverance] -> HS -> [IR + Berserk] -> FC -> Infuriate -> FC -> [Vengeance] -> Maim -> [Brutal Swing] -> Eye -> HS -> Maim -> Eye -> Fracture -> FC -> Pacified

I'd still recommend using Berserk + IR under Unchained for the extra enmity, but purely damage-wise that would be your highest.