My guess is they were looking for a little more power out of a corner infielder; Boggs only hit 9 homers in 6 minor league seasons and until his last year in AAA, there weren't a lot of doubles either (71 total through his first 5 minor league seasons). His last year at AAA, he hit 41.
Boggs was a late bloomer. He was a 7th round pick, so it's not like he had star written all over him out of high school. Some guys take longer to figure it out; maybe he just had to mature physically.
He was an anomaly in that he hit better in the majors than he did in the minors (although he did hit pretty well for average there as well), When he first came up (1982), he played as much 1B as he did 3B; the Sox had Carney Lansford at 3rd and all he had done was win the batting title his first year with Boston in 1981 (and he still hit .301 in 1982).