How poor of a shortcut is it? I'm not really clear on what the math would look like. Would it just be better by approximately the ratio of gravity's strength at the surface vs the height of the balloon?
Better than the miniscule gain in potential energy (height x mass x gravity) because you also save a lot of aerodynamic drag not punching through the lower atmosphere at high speed and some "hovering losses" (rise time x mass x gravity, I'm sure there is a better term for that). But still not worthwhile due to the difficulty of floating a full size rocket. If you had a very very high mountain or tower, moving that full size rocket to the peak could be worthwhile. Theoretically, a civilisation trapped in a gravity well too deep for a solution to the rocket equation could dig themselves out by reshaping their planet from a roughly spherical geoid into a disc or rod (or into a torus for the really adventurous)
Basically just saves what you would've lost to wind resistance and gravity while getting to that height, while adding the complication of accelerating from 0 to orbital before falling back into the atmo.
Space elevator ideas usually have the hop-off point all the way out at geosynchronous orbit to solve the velocity problem. Which is.. a really tall elevator.
