After seeing this question, I was struck with an intense curiosity to know:
Were there ever processors with word sizes that aren't powers of two, specifically after the 8-bit byte became the industry standard? (I'm well aware of the 9-, 18-, and 36-bit computers that predate the 8-bit byte.)
I've seen some things that are close to this, for example the PIC24 series of 16-bit processors that uses a 24-bit instruction word, but I'm not aware of any actual 24-bit (etc) processors.
If not, why not? I can think of a few possible downsides, but I'm not knowledgeable enough about the history to actually know.