In this video a glider is pulled up by a winch on the ground, like this:
I would say you could apply the same principles with bigger planes, possibly even using sustainable energy sources.
The plane would not use its engines at all to get to cruising attitude (unlike a suggested catapult in a previous post), so this part of the flight would be "for free". Using a back of the envelope type of calculation with 5% efficiency it takes 17000 litres of kerosine to lift a 747 to 10km (which agrees with this paper).
However, this would however cost at least (calculated below) 25km of towing line(s). If we use a UHMWPE fiber a 400g/m and 1.2 cm radius cable would be able to support 2x the 400kN thrust maximum output of a typical airliner.
Sure there are a lot of hurdles to overcome, but since some airports in cities cannot expand because of noise problems this seems like one solution.
Logistically this seems like a large extra challenge for the crew on the ground, but would this be possible?
I'm still not convinced this is impossible, while not useful for less densely populated areas this could be useful for densely populated countries:: It's not impossible; anything can be done if someone has the will. But cable-launching heavy aircraft has very little usefulness, no matter the population. Why do you think it could be useful in densely populated areas? $\endgroup$