I still wonder why they couldn't have the Enterprise scanning the wreckage of the fleet for survivors. Scotty, being the chief engineer of the Farragut, gets beamed aboard, and overhears a report that the Enterprise's chief engineer has been killed. He immediately walks to Spock, explains his love and knowledge for the Enterprise ship class and convinces him he's the best for the job.
Kirk isn't exiled, he's put in a brig. The "out of your Vulcan mind" dialog between McCoy and Spock would have been the same. Old Spock walks to the outpost on Delta Vega, witnesses the destruction of Vulcan, and recognizes the Enterprise on sensors. He actively contacts the Enterprise, requesting "Captain James T. Kirk" with "information about the Romulan Nero" and requests a meeting with Kirk in the outpost.
Young Spock ponders about that, and then decides to give it a shot. Kirk is beamed down alone. Old Spock wonders why Kirk isn't Captain, mindmeld, tells Kirk he needs to take command, Kirk beams back, gets on Young Spocks nerves, breakdown, rest of the film is the same.
This would have worked much better IMO.
Or rather than "love and knowledge" (or essentially the same as it), Scotty could have been the ranking qualified officer still left alive, just like McCoy.
I agree that the Delta Vega segment in the film seemed especially half-baked.
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But with respect to the topic of this thread, improving the plot, or even dramatically improving it, to repair weaknesses isn't the same as plugging nonexistent plot holes, when there are no holes per se.