It also takes a lot of heavy rocket fuel to get a heavy rocket up that high.
And then you need more heavy rocket fuel to get all that heavy rocket fuel off the ground.
It's been done, and is a relatively routine method to get really high results out of test/sounding rockets. However, something more substantial like satellite launch etc. where you've got a precise launch window to hit, it has some disadvantages.
The downward momentum when the rocket is released that needs to be overcome robs you of some of the 20-odd miles up and atmospheric friction you've "saved" on, as does the weight of an aggressively gimballing engine, and flight control system that can quickly orient the rocket to it's proper trajectory once dropped, or recover well if it doesn't maintain a suitable attitude when it's released.
Although maybe being able to get the "rockoon" released right at the equator, maybe with some prevailing easterly winds would give you even more savings.
The main disadvantage of course is if the rocket doesn't light. On a traditional launch pad, there's good odds you can fix things and try again. With a rockoon, not so much.
An old idea that could perhaps get revamped a bit?
http://youtu.be/96A0wb1Ov9k
Hmm... Any of the stuff we wound up giving up on because it was "too destabilizing" for MAD with Russia, and first-strike capabilities is probably what we should have been doing. USSR might have bankrupted itself 10 years earlier.
Although not that different in concept than the under-wing Pegasus boosters used from B-52's for satellite launches.
