This principle is already in use in "Ski-jump" aircraft carriers[0] like the British and Chinese use, compared to the catapult operated American carriers. The problem is it isn't remotely high enough. It does have an effect on take off distance, so for that short amount would help for fuel efficiency, but then you still have +30,000ft to climb. 737's often cruise at 30-40k feet, as the air is thinner up there so there's less drag and you have better fuel efficiency. Even if you launched airplanes off the tallest structure ever built (Burj Khalifa, 2,700ft), you'd still have the majority of the climb ahead of you. Planes go high.
My non-credible idea would be to just use an Apple-style magsafe charger on the back of the airplane that disconnects midair at 30,000ft and falls on the helpless people below.
Yeah, I didn't check to consider that the specific potential energy (10 km times g = 100 kJ/kg) is actually much larger than the specific kinetic energy (200 m/s squared over two = 20 kJ/kg) so my idea of pre-charging the velocity doesn't pencil out.
I do like the magsafe charger idea. However, I anticipate some regulatory issues.
My non-credible idea would be to just use an Apple-style magsafe charger on the back of the airplane that disconnects midair at 30,000ft and falls on the helpless people below.
[0] https://en.wikipedia.org/wiki/Ski-jump_(aviation)