Currently it can be used exactly one time. ... Yay!
As the AI does not use gates anyway, even though their activation has been in the game for several versions, let us use the thing to move around already-deployed gates as well. There are always some in locations where they are absolutely useless.
... Factions should probably be upset, if you steal their gates, useless or not. Bonus points, if they get even more upset after 'At the Gates', once everyone knows that the gates can be reactivated right now.
Maybe lock the option in claimed systems behind owning a High Command (and thence presumably being able to defend the thing while it does its thing).
Once the campaign progresses to the point where AI fleets also use gates, this could be the starting point for additional emergent events, namely factions trying to capture the Gate Hauler and, if successful, stealing gates for themselves, or staging system raids targeting not (only) planets but also gates, with Gate Hauler and escort fleet in tow and hostile reaction force rallying on the opposing side in a "king of the hill" style scenario.