You are carrying fuel and using oxygen from the atmosphere to combust it. When it's hot, it's a gas. By simply cooling it and recovering most of it, you are potentially left with more mass than you started off with... and Oxygen is relatively heavy.
Why not just take on some liquid water at the destination when you drop the cargo?
Storing higher humidity air doesn't sound very efficient, storing liquefied humid air sounds like a disaster waiting to happen, and storing compressed air sounds like an unnecessarily complicated alternative to just compressing the hydrogen.
Fun fact: many inclined elevators work this way :)