It has a few other advantages
It lets you 'launch' from the best point on Earth for the orbit you require without worrying about where you can build a space center.
You can launch in any weather, there isn't much weather >50,000ft to mess you up.
It's easier to build a rocket that only has to operate in very sparse atmosphere than one that has to manage both thick sea level and sparse high altitude conditions.
Steering the rocket is also much easier, at altitude you don't need the high degree of rapid directional control that is needed to get it past the launch tower and clear of surface winds.
This is already being done with the Pegasus system - with a rocket released from under a converted airliner, Virgin Atlantic is also looking at a launch from it's high altitude test aircraft.