Powers of two are more natural in a binary computer. Then add the fact that 8 is the smallest power of two that allows you to fit the Latin alphabet plus most common symbols as a character encoding.

We're all about building towers of abstractions. It does make sense to aim for designs that are natural for humans when you're closer to the top of the stack. Bytes are fairly low down the stack, so it makes more sense for them to be natural to computers.