ASCII has its roots in teletype codes, which were a development from telegraph codes like Morse.
Morse code is variable length, so this made automatic telegraph machines or teletypes awkward to implement. The solution was the 5 bit Baudot code. Using a fixed length code simplified the devices. Operators could type Baudot code using one hand on a 5 key keyboard. Part of the code's design was to minimize operator fatigue.
Baudot code is why we refer to the symbol rate of modems and the like in Baud btw.
Anyhow, the next change came with instead of telegraph machines directly signaling on the wire, instead a typewriter was used to create a punched tape of codepoints, which would be loaded into the telegraph machine for transmission. Since the keyboard was now decoupled from the wire code, there was more flexibility to add additional code points. This is where stuff like "Carriage Return" and "Line Feed" originate. This got standardized by Western Union and internationally.
By the time we get to ASCII, teleprinters are common, and the early computer industry adopted punched cards pervasively as an input format. And they initially did the straightforward thing of just using the telegraph codes. But then someone at IBM came up with a new scheme that would be faster when using punch cards in sorting machines. And that became ASCII eventually.
So zooming out here the story is that we started with binary codes, then adopted new schemes as technology developed. All this happened long before the digital computing world settled on 8 bit bytes as a convention. ASCII as bytes is just a practical compromise between the older teletype codes and the newer convention.