Having 6-bit bytes on a CDC was a terrific PITA! The byte size was a tradeoffs between saving MONEY (RAM) and the hassle of shift codes (070) used to get uppercase letters and rare symbols! Once semiconductor memory began to be available (2M words of 'ECS' - "extended core storage" - actually semiconductor memory - was added to our 1M byte memory in ~1978) computer architects could afford to burn the extra 2 bits in every word to make programming easier...
At about the same time microprocessors like the 8008 were starting to take off (1975). If the basic instruction could not support a 0-100 value it would be virtually useless! There was only 1 microprocessor that DID NOT use the 8-bit byte and that was the 12-bit intersil 6100 which copied the pdp-8 instruction set!
Also the invention of double precision floating point made 32-bit floating point okay. From the 40s till the 70s the most critical decision in computer architecture was the size of the floating point word: 36, 48, 52, 60 bits ... But 32 is clearly inadequate. But the idea that you could have a second larger floating point fpu that handled 32 AND 64-bit words made 32-bit floating point acceptable..
Also in the early 1970s text processing took off, partly from the invention of ASCII (1963), partly from 8-bit microprocessors, partly from a little known OS whose fundamental idea was that characters should be the only unit of I/O (Unix -father of Linux).
So why do we have 8-bit bytes? Thank you, Gordon Moore!