I would put most of the popularity for word lengths that are powers of 2 on the IBM System/360 (1964), rather than the PDP-11 (1970). The enormous popularity of the System/360 is what made computers standardize on bytes, along with words that were multiples of bytes. Prior to that, word sizes were all over the map: 6, 12, 36, as well as really random values such as 23, 27, 29, or 35 bit words.

This isn't to deny the popularity of the PDP-11, of course, but its use of 16-bit words was more of a consequence of the System/360. DEC's use of 12-bit words goes back to the LINC (1962) but by 1970, bytes were obviously the way to go.