An additional factor that I didn't think of earlier: there have been ships crashing on the planet, thanks to Krall's activities, since the Franklin (which was probably the alpha shipwreck) went down. It's implied a considerable number of them. When Edison and his crew crash-landed, there weren't other vessels around to scavenge spare parts from. By the time Jaylah was stranded, there clearly were. Edison and his crew had to bet fully on the alien tech already present to get off-planet, and by the time they really learned how to use it the Franklin was an obsolete hulk to them.I'm going to have to look for an explanation I may have missed when I see it again, but the question for me is why Edison's crew couldn't have gotten the ship back into space themselves in the time after the crash.