Looking at the Apollo 13 mission timeline within three hours after the explosion of O2 tank two all oxygen in the SPS was completely depleted. Fuel cells #1 and #3 were off line. CM had even started to cannibalize its reentry batteries, before it was shut down. The damage to the SPS was unknown and deemed unreliable
(you couldn't fire it with the LEM attached anyway) [see comment]. It seems to me that, at that point, the Service Module had no resources that were of any use anymore.
What were the reasons NASA opted to keep the SM attached for the rest of mission? I would expect that attitude and trajectory control would have been much easier without hauling the dead SM around.
The only explanation I could think of was to protect the CM's heat shield from direct exposure to space?