That's a trickier one we have discussed. I can bring it up for discussion again. She has warning FX associated with it that may prompt users to burn X tool to try to respond. On interrupt she would get to use it again now on a target who now lost that tool. Especially for something coming over a wall, imagine using Aegis as you know you are about to die to Da Ji (you wait til the last possible second) and it doesn't come, only to suddenly happen again 1s later. There is often a feedback issue due to the abilities function which prevents the person being affected from knowing why or why not an ability went off.
This argument can be expanded out to other abilities where we give the cooldown back but they often lack the hard warning FX and common situations that Da Ji creates. Its a situation where Hard Rules vs. Use Cases create some murky waters.