You seem to fundamentally ignore the point that not playing any PGs as backups to Exum means Burks having to play a majority of his minutes there. Is playing 70% of Burks' minutes at the 1 offensively (and defensively) better than having him play mostly at the 2? Is playing Hood less minutes better for our offense than playing Carroll?
This is more about signing Carroll and its negative ramifications on the roles of two of the most promising young wings in the NBA this coming season-- as opposed to robbing the playing time of Burke and Ingles. Both players are competent back-ups, and both can have their contributions easily overtaken by other promising players on the roster later in the season if they blow it. NBA teams don't roll 12 deep.
See above. Our offense has much more potential by giving lots of playing time to multiple playmakers with versatile scoring repertoires than giving it to a true SF when we already have a damn good one to begin with.
Or because of the fact that playing 70% of Alec's minutes at the 1 would be stupid, and it would neuter the huge contributions he could have with the team next season.