However, it then raises the question: What are they doing on aircraft carriers and how is that different ?
https://en.wikipedia.org/wiki/Aircraft_catapult
... I assumed those had some fuel-use benefit, but perhaps their only benefit is shortening the runway ?
You could likely lessen fuel burn of a supersonic aircraft taking off (as you could with a subsonic aircraft) by accelerating it via a catapult of sorts, but you have to do so at acceleration levels tolerable to all passengers, which would make for a long, unwieldy catapult. Release speed is also obviously going to be very subsonic.