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This is entertaining and probably a good idea but the justification is very abstract.

Specifically, has there even been a C++ compiler on a system where bytes weren't 8 bits? If so, when was it last updated?

There were/are C++ compilers for PDP-10 (9 bit byte). Those haven't been maintained AFAICT, but there are C++ compilers for various DSP's where the smallest unit of access is 16 or 32 bits that are still being sold.
I know some DSPs have 24-bit "bytes", and there are C compilers available for them.