Disagree. The Brotherhood would never discover the "entrance" without the player. So the institute could use their teleporter to destroy the brotherhood in hit and run raids. Hell if they had any tactical sense they could just teleport a nuke poof brotherhood problem gone.
Control of the skies is as pointless as calvary power in WWII when the enemy can arrive anywhere in the Commonwealth at an instance notice.
Example they teleport to a building a block away from the airport set up a low yield nuke (not a mini nuke) and boom the brotherhood is dead. What is worse is that all the prep work to set the bomb off could be done a hundred miles away or more then teleported to the sight and boom no long countdown needed to let people escape just set it for 10 seconds and poof you are gone and so is teh brotherhood.
What defence is there against this? The BOS can't win without the player because they have openly declared themselves enemies of the institution without taking steps to HIDE from the institute's retaliation.