The energy for launching the body at the catch is used in the second part of the drive to pull the handle and bring your body to a standstill even before the final pull with the arms.
"Used in the second part": only if we pull the handle, which is in itself work done. Kinetic energy can be recovered only by storing it as potential energy (height) or in something elastic. Examples are pendulums and rubber balls.
We are not like these. In their absence, to change the direction of motion is an acceleration, so requires work; the typical example is driving a car round a hairpin bend. If we don't open the gas, the car decelerates, i.e. does work and loses energy. Running in circles is much harder than going straight: speed may be constant, but not velocity, so it's continuous acceleration. Skipping woud be a cinch if we could stay rigid and bounce off the floor.
Another example is walking downhill. This can be very hard work, despite the help we get from gravity, because we have to stop ourselves; using muscle in eccentric.
There's no point in comparing bike and rowerg power: use of most muscle groups including small ones in sequence, transmission through arms back and shoulders, different training, need to accelerate body mass, long times when no energy is being delivered to the handle, limits to peak force, dodgy technique together ensure that rowing is not an efficient way of delivering power.
All we can do to improve efficiency on an erg is put it on slides and learn to row without spurious action, like any good crew.
So what, it gets us fit anyway, and maybe more so, thanks to the use of more muscle over a wider range of movement.
08-1940, 179cm, 75kg post-op (3 bp).