(Yesterday, I finally got around to making encoding_rs work on 64-bit big-endian systems by testing PPC64 in qemu. Then I timed out trying to get a 32-bit big-endian system with recent enough glibc to run Rust up and running in qemu, so I still haven't tested the 32-bit case... Unclear if anyone even cares.)
I develop crypto code. Testing on BE is nice, not just because of endian neutral code but testing on something 'weird' can turn rare faults into common ones.
Beyond endianness I've found interesting bugs by running code on HP-PA (stack grows in the reverse direction) and on Itanium (misalignment causes a trap to the kernel)...
I wish there were a qemu supported fake architecture that made every optional decision differently (or at least every one that works with most code...).