For the ref there are a couple video available on youtube that showcase a "pure" back butterfly swimming (imho not that succesfully).
At distance pace a narrow whip kick help to dive in the water as the hands enter and make a for low SPL, as one accelerates more power is directed toward the arms, SPL increases, etc => as for the version swum on the breast, the dolphin kick become a more pertinent solution.
As a side note the whip kick blends in the stroke much much better on the back than on the breast. A "funny" thing is that on the back you can swim "complete" breastroke with complete arm movement as airborn recovery is a given.
To summup I like swimming on the back, it works pretty well and both my neck and back thanks me in return.