According to my friend Russ Robulen (his coworker, lead on the 360/50, worked on /91 and later lead for the IBM ASC),  Amdahl wanted the byte to be 7-bits for S/360, but Fred Brook's overruled him.  Brooks was said to have thrown Amdahl out his office and told him "not come back unless it was a power of 2", as "he could not program it sanely otherwise."   Amdahl semi-won the 24/32 bit war.   Brooks let he have a 24 bit basic word, only if it stored it as 32 bits and ensured that all pointers were stored in the same.  Russ says that Amdahl always thought both choices were a terrible waste of hardware.   Gordon Bell later said, those two choices were the most important in S/360's lasting impact.

Clem