There were several different coding systems for characters around. The best known (alive up to this day) was IBM's EBCDIC, but most any manufacturer had their own. We had a DEC 2020, which handled several different character coding systems with it's 36-bit (!) words, a 6-bit DEC own, at least one 7-bit one (I think it was ASCII, with no parity bit) and 8-bit ones. If I remember right, it handled EBCDIC too, for IBM compatibility. All in the interest of scrimping a few bits per character (memory was precious in the '70es!).
Defining a character code of some sort was clearly a requirement if you wanted to read/write anything that wasn't just numbers, and that means agreeing on some mapping of (a subset of) the characters in use to numbers (the natural language inside the computer). You can get away with e.g. 6 bits (64 possible characters) if you restrict yourself a lot, ASCII's 7 bits (128 possibilities) is very cramped (specially if you want to write some non-English text, or even such English words as rôle, naïve, fiancé or others borrowed from other languages).
Even the prehistoric Morse code is a coding system for characters, just not in numbers. See also character encoding for it's history.