I don't know that 7-bit bytes were ever used. Computer word sizes have historically been multiples of 6 or 8 bits, and while I can't say as to why particular values were chosen, I would hypothesize that multiples of 6 and 8 work well for representation in octal and hexadecimal respectively. For many of these early machines, sub-word addressability wasn't really a thing, so the question of 'byte' is somewhat academic.

For the representation of text of an alphabetic language, you need to hit 6 bits if your script doesn't have case and 7 bits if it does have case. ASCII ended up encoding English into 7 bits and EBCDIC chose 8 bits (as it's based on a binary-coded decimal scheme which packs a decimal digit into 4 bits). Early machines did choose to use the unused high bit of an ASCII character stored in 8 bits as a parity bit, but most machines have instead opted to extend the character repertoire in a variety of incompatible ways, which eventually led to Unicode.