I understood that the configurations currently in use usually only power up either the big or little cores at the same time, and that kind of migration has to wipe the caches, right? But that might be inaccurate, and you are of course right in the general case.

The state of the art in Linux scheduler handling of big.LITTLE hardware has moved through several different models, getting steadily better at getting best performance from the hardware (wikipedia has a good brief rundown: https://en.wikipedia.org/wiki/ARM_big.LITTLE). You're thinking about the in-kernel-scheduler approach, but global task scheduling (where you just tell the scheduler about all the cores and let it move processes around to suit) has been the recommended approach for a few years now I think.