It's not that the Sox didn't care about hitting or didn't try to get it. Some of the players they thought were going to do very well (Ken Berry immediately comes to mind) never became the hitters they thought they were going to be.
They became good players with exceptional defensive skills for the most part, but just never could hit like other players on other teams.
Also factoring in were the fact that Comiskey Park was not a hitters park by any means and the 'frozen baseballs' in the mid 1960's.
As stated the Sox knew what they were lacking and made serious attempts to get players like Frank Robinson, Yaz and Hawk Harrelson on to the team...to no avail.
I'll return in a minute posting a link to the story I posted that has the details of those 'near misses'
And I agree 1967 was a great year, Stanky almost pulled off a miracle but the 1964 season was better with a better club and a better team.
1964 started to slip away when the Sox lost a double header to the lowly washington Senators who started Bennie Daniels and Dave Stenhouse. Two pitchers with bad records (although Daniels wasn't a bad pitcher...)