I agree entirely with @lowwall .Drag. If you are moving at all, the frog kick blade path results in much higher drag than flutter.
I don't know what "return the energy back to the water" means. Frog's perceived efficiency is almost entirely a byproduct of its low speed. Throttling flutter back to frog speeds results in greater efficiency.
Frog kicks does have advantages, but efficiency is not one of them.
When I became a finned swimming instructor I had to make a number of experiments for finding the most efficient kicking style and the corresponding best type of fin(s) for each athlet under my supervision.
The result was invariantly the same with all athlets I worked with: whilst the fastest style is dolphin kick with a monofin, the most efficient style is flutter kick with modest amplitude and long flexible carbon-fiber fins.
This is the way an athlet can travel the longer distance with a single breath.
The optimum efficiency was reached by each athlet at his own optimal speed, and with a personal optimal choice of fin's length, stiffness and angle between blade and foot.
So there is no "best fin for everyone".
Athlets coming to finned swimming after years of frog swimming without fins were often convinced that frog kicking was more efficient also wearing fins. It did usually take me a dozen of hours or more of work in the pool for proofing them wrong.
It is first necessary to teach them how to flutter kick properly. Often people used to good frog kicking have a terrible flutter kick, they use just half of the kick for active propulsion (usually the down kick), using the other part of the movement just as a "recovery".
But there is no recovery in a proper flutter kick (even if modified for keeping the fins away from the bottom): both down and up motions are fully active.