Yeah, its a problem... I woke with the thought you may as well launch in pairs over a counter weight.
The thought of simultaneous release has a very large problem in a vertical launch, the pit for the downward trajectory blast being one...
But Elon certainly has shown he can hire the right people for the projects and he can run large scale testing at comparatively low market costs.
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A rocket that can hold high altitude would be a major part in any sky elevator project. If you can fling that rocket to 75km, it only needs enough fuel for maintaining altitude and some course corrections to allow hooking onto the sky crane and get the payload to load space.
Such a system would see space hardware/resupply launch costs reduced pretty dramatically.
International Academy of Astronautics published "Road to the Space Elevator Era", seems to suggest is closer than nuclear fusion at least.