First off, you can do any kick in split fins, including back kicking. I think it might be quite difficult to LEARN some of the kicks in splits, but I have done a dive in splits after I learned the kicks, and they are all possible. They feel funny, and the back kick isn't as efficient, but they're doable.
Second, if you are swimming into current, the frog kick is an awful kick. This is not me speaking; this is David Rhea, who is one of the most experienced cave divers there is, and who dives extensively in Florida caves where you work against strong flow. The frog kick's central characteristic is a glide phase. Using a kick with a glide phase against water flowing toward you is less effective, because during that phase, you are slowing down or even moving backwards. The flutter kick provides propulsive force all the time, and works much better in current or flow.
If you look at paddle fins versus splits, one of the big differences is stiffness. As you move your foot through the down or upstroke of a flutter kick, the stiff fins will continue to "bite" the water and provide propulsion. However, splits will flex, and once they have flexed maximally, they provide no further resistance to the water, and therefore no further forward force. So the leg excursion which is creating propulsive force is shorter, and the frequency has to be higher, in split fins. The effort expended by your muscles per stroke is lower, but the number of strokes required to cover a given distance is greater.