Story wise, might not make sense. Mechanically wise, frustrating as all hell. That being said, we have our ghost by the time of the strike, and out ghosts are powered by light. This would mean we have some form of connection to the traveler again, and this is reinforced by Zavala saying, "If the light can find its way back to you, perhaps there's hope for us all." (https://youtu.be/kmFGetMZi6s - Destiny 2 Gameplay Premiere) Supers do seem to take forever, and at this point we haven't been shown a way to decrease cooldowns. Most likely this will be tied to weapon and/or armor mods, but it's a bit of a let down not being shown these things in the Beta.