We could, but it would require new aircraft. Passenger aircraft are not designed for that kind of stress. I'm not sure that passengers would like that much acceleration either.
I don't know that it would actually save anything though. Aircraft of carriers are held back while they throttle the engine to full throttle. Only after the pilot is convinced the engine will run long enough to take off do they release the brakes - probably using more fuel than a regular takeoff. (the other option is to get in the air and then discover the engine isn't running and so you crash land a few meters later). I'd want a real aircraft engineer to speak to this.
You could save some energy by catapulting a plane at a reasonable acceleration, like a glider is launched with a ground tractor wire. I flied gliders this way and I think the acceleration was not worse than a regular airliner. Problem is, the saving is not worth the cost and complexity.
The carrier example is wrong, the planes stay on the catapult only a few seconds while they go full throttle (this takes time), even with the burn rate it is not a significant quantity of fuel. Regular planes can do the same on the runway, I did it myself several times for fun, but it rarely bring benefits - the only place where it helps is with very short runways. In any case, the fuel consumption is not significant.
How about you elevator passengers up to a runway that is a thousand feet up in the air. Then use electric lines on the runway to power the takeoff to avoid using any onboard batteries until airborne. Just daydreaming here a bit!
It is easy, you put small BLDCs in the wheels. No need to push on air while you are on the ground. You could also have basically a super car drone or a maglev rail under the plane, launch it into the sky.
I don't know that it would actually save anything though. Aircraft of carriers are held back while they throttle the engine to full throttle. Only after the pilot is convinced the engine will run long enough to take off do they release the brakes - probably using more fuel than a regular takeoff. (the other option is to get in the air and then discover the engine isn't running and so you crash land a few meters later). I'd want a real aircraft engineer to speak to this.