Does it now mean: balloon "fahren" or balloon flying / balloon ride or balloon flight?
Why you fly balloons and not balloons can be explained in a few very plausible sentences:
We travel with the wind in a balloon; that is, we move with the current that the air mass has. A balloon cannot fly because it has no engine or anything like that. Our destination is determined by the wind alone. Of course we can set and hit targets, but to do so we have to study and take into account the wind model predictions.
A balloon has no wings to give the object lift. This in turn puts the balloon in a category of its own. The hot-air balloon rises, because by heating the air in the envelope, you achieve a lower density; the lower the density, the lower the weight. Warm air therefore becomes lighter and rises. The gas balloon is filled with a gas that also has a lower density than air. Therefore this balloon also rises and travels with the wind...
Comparisons are always good: As an understandable example I often use the comparison with a sailing ship. As is well known, a sailing ship also travels with the wind. The ship also has no wheels. The ship, just like a balloon, moves forward in the current of the wind - actually, the expression "ship-swobbing" would be more logical than "the ship's journey". Yet no one would think of changing that...