Netbsd releases big endian versions that work on various ARM boards. Here's an announcement showing it works on an Rpi3 and below, for example: https://mail-index.netbsd.org/port-arm/2020/12/03/msg007117....
They said at the time that it's not yet working on the Rpi4 because of issues getting BE mode and UEFI to work together.
I don't know that it's used often, but it does exist.
Or perhaps very slightly more efficient networking code, since big endian is the default order for many operations there?
Their close cousins the RM57 line look like nearly identical parts that are little-endian. I believe, but cannot prove, that the only difference in silicon is a factory one-time-programmable setting (fuse).
"Why would anyone want to build a BE machine?" In this case, they are trying to gain market-share from big-endian POWER microcontrollers.