Unless Shadow goes 6 turns in a row, there is nothing it can do when Edge EX is up and the mirage buff is on to mask everyone from getting hits.
The best part of Edge coming after Bahamut is, you can just instantly get a EX, or save a EX later for a rainy day and not get hit at all.
Technically Galuf can sub Garnet such that when Shadow's C88 and Galuf's evasion buffs are on, they can all dodge and counter without needing Edge's EX. I am sure a full dodge squad like that is fairly destructive as well.
That said since Shadow has the benefit of getting 3 turns after dodging and countering, it seems really nice to take advantage of that in the form of building Garnet stacks and trigger another off-turn attack while you are on active offense instead of just waiting for the boss to move.
Since the boss orb is non-lethal and triggers every 5 turns, it is almost guaranteed that Shadow will get to go again and thus trigger more Garnet's Ark off-turn attack. The orb is an AoE attack, so it also procs both Edge's and Shadow's counters at the same time. When the boss teleport the adds' turns to the front and get dodged, it simultaneously build stacks for Garnet and trigger additional counters.
So no matter what the boss does, it just kills itself faster by doing practically anything.
This also happens to be a blatant weakness of the Safer Sephiroth fight. It can also be completely cheesed with dodge & counter and myriads of off-turn attack triggers with crit buff CAs on. He AoEs alot in his consecutive turns as well so he just kills himself even faster.
Edge + Bahamut is just a very nice clutch and abusable combo in certain situation and its effect is further expended by Shadow's dodge interaction with Garnet LD's mechanic. There are a lot of ways you can combo these effects and they are indeed very fun to mess around with.
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