One example from the software side: A common thing to do in data processing is to obtain bit offsets (compression, video decoding etc.). If a byte would be 10 bits you would need mod%10 operations everywhere which is slow and/or complex. In contrast mod%(2^N) is one logic processor instruction.

Eight is a nice power of two.

I'm fairly sure it's because the English character set fits nicely into a byte. 7 bits would have have worked as well, but 7 is a very odd width for something in a binary computer.

If you're ignoring what's efficient to use then just use a decimal data type and let the hardware figure out how to calculate that for you best. If what's efficient matters then address management, hardware operation implementations, and data packing are all simplest when the group size is a power of the base.

likely mostly as a concession to ASCII in the end. you used a typewriter to write into and receive terminal output from machines back in the day. terminals would use ASCII. there were machines with all sorts of smallest-addressable-sizes, but eight bit bytes align nicely with ASCII. makes strings easier. making strings easier makes programming easier. easier programming makes a machine more popular. once machines started standardizing on eight bit bytes, others followed. when they went to add more data, they kept the byte since code was written for bytes, and made their new registeres two bytes. then two of those. then two of those. so we're sitting at 64 bit registers on the backs of all that that came before.

I'm not sure why you think being able to store values from -512 to +511 is more logical than -128 to +127?