The Sox absolutely needed another bat.
But when JD plays RF over Mookie (on those rest days), the difference just becomes beyond obvious. The game in Toronto gave a pretty good example there, where Smoak hit a soft liner to right field to move a runner to third. Even if Mookie was unable to catch that ball (which I doubt but can't prove), at the very least the runner would have had to hold up enough to make sure and would not have been able to go to third....