non-ARM-manufacturer citation needed :). My experience as a compiler guy (that makes the toolchains for these kinds of phones) has been that big little brings improvements to what these guys can shove on a chip and advertise, but so far not real improvements to battery life or real numbers.
There reason why is pretty simple.
In an ideal world, you don't want anything running at all. You don't want A53's "handling the majority of the workload". What you want is to wake up, do whatever work is needed as fast as possible, and go back to sleep. Period. Sleeping chips are lower power, by far, than idling chips.
If it's faster to do that work with an A57, it'll generally give you better battery life to do that. Again, this is right now, based on perf per watt/blah blah blah. Maybe someday, in the future, a53's will be so low power vs a57 that doing something else makes sense. But it's not true now, AFAIK.
Instead, they make big-little because they can't really increase the speed of the higher end cores more without increasing power usage too much.