Edge/Flood of Darkness/Shadow share a cooldown timer, why?

[Dualblade]

Edge and Flood are mainly ment to get your darkside buff. Any extra you get in beyond maintaining it is to your gain.

They also gave us two so we had one for an oGCD version for single and AoE situations, which is important because they made the single-target the more powerful one. If they had just made it combo off either Unleash or Dark Passenger would mean it would also have to only be an AoE version, and thus the less powerful one. Which depending on they did it would be fine for the DP one but personally I like the way Edge and Flood work right now.

The only thing I don't like is that Flood doesn't use DP's animation. I understand why, Flood's animation is both much faster AND looks like Cecil's Darkness skill which both DP and Flood are based on, but I still liked the DP animation.

[Cosaint]

Its an additional refresh button, its existance is entirely built upon that one "situation" it could do anything else, and still be an aoe supplement. They got rid of ultimatum, can you tell me why? Ill tell you why, we already had single target provoke.

Your comparison doesn't make sense. Edge and Flood are both useful skills and a DPS gain when used correctly.
Ultimatum was completely useless outside some very niche uses that could be circumvented through the use of Provoke. Basically it got cut as players didn't feel the need to use it. That is not the case of Edge/Flood of Shadow.

[Seraphor]

Edge and Flood aren't simply Darkside refresh buttons though, they're pretty powerful attacks in their own right, and the definitely makes a difference in single-target/trash-pull contexts.

[Lyth]

Edge and Flood both have a 2 second recast. That's likely there to prevent you from doubleweaving these abilities with themselves for 1000+ potency. The shared recast is likely there for a similar reason.