While it would be fun, cool, <insert adjective>, using a catapult or whatever is pointless in the grand scheme of things for the total energy budget required for air travel. The energy to accelerate a vehicle to flying speed is nothing compared to the energy required to climb to cruising speed. Everyone that drives an EV intuitively knows this already. We don't estimate energy loss to do a one-time acceleration to highway speed, but we do plan for elevation gain required to cross a mountain pass.
Putting actual numbers to it. The formula for kinetic energy is "1/2 m v^2" and the formula for potential energy due to gravity is "m g h". In both cases, m is mass so the relative scale of the numbers doesn't change if we're talking about a small business jet or an Airbus A380.
In the kinetic energy formula, v is velocity in m/s. An airline lifting off at 200 mph is traveling at just shy of 90 m/s. Square that and take 1/2 and you get roughly 4,000 as the number to multiply by the mass for getting the kinetic energy.
An airline flying at 32,800' above ground is 10,000m above the ground, which is h in the potential energy formula. g is gravity, which on earth 9.8 m/s^2 - call it 10 to make the math easy. That means that potential energy for an airline in cruising flight is 100,000 times the mass.
This means that it takes 25 times as much energy for an airline to climb to cruising altitude as it does to accelerate to flying speed on the ground. You could accelerate to a higher speed, but you're still not even within the same order of magnitude compared to the energy required to climb to altitude. I understand that this probably should be an integral of some sort to figure out the true energy required as fuel is burned off in the climb, but this simple calculation gets you in the right ballpark and the two energy buckets aren't even in the same order of magnitude, so everything else is probably inconsequential.
This difference in energy input requirements is also intuitive in that an airplane can accelerate to flying speed in a minute, but it takes 10-20 minutes to climb to flying altitude.
Kinetic Energy Calculator -
Kinetic Energy Calculator
Gravitational Potential Energy Calculator -
Gravitational Potential Energy Calculator