Warning: The following contains SPOILERS for Legends of Tomorrow season 6, episode 7 "Back to the Finale: Part II"
The Legends of Tomorrow episode "Back to the Finale: Part II" offered an explanation for a question many fans had been asking since the season 6 premiere; why didn't the Legends use time travel to prevent the kidnapping of Sara Lance? Some felt the team's failure to consider this option represented a major plot hole, given that it should have been easy, give the circumstances, for the team to save Sara without causing a paradox. However, the events of "Back to the Finale: Part II" explained why this wasn't feasible, upholding the tradition of earlier episodes such as "Here I Go Again" and "Legends Of To-Meow-Meow," which also showcased the difficulties in using time travel in the Arrowverse to prevent a disaster.
Legends of Tomorrow's season 5 finale, "Swan Thong," ended with Sara Lance apparently being abducted by aliens after leaving a London punk club in 1977. The rest of the team failed to notice this until the next morning (and the season 6 premiere) as most of them were highly intoxicated or highly distracted. Even after they figured out what happened, the Legends had no way of tracking Sara until they began detecting the time anomalies created by the aliens Sara released into the Temporal Zone while trying to take control of her captors' ship. This left the Legends averting the paradoxes caused by the time-displaced aliens over the course of season 6, while searching for clues on where and when Sara could be found. However, several fans pointed out that there was nothing to stop the Legends from using their time-ship to go back to the night of Sara's abduction and chasing after her abductors once she was taken.
While this would have kept the chain of cause and event intact, it's doubtful that rescuing Sara Lance would be as simple as chasing after her kidnappers. This point was driven home by the episode "Back to the Finale: Part II," in which all of the Legends (save Ava Sharpe) went back in time to the night of Sarah's abduction. Rather than pursing her kidnappers, however, they tried the much simpler and safer approach of trying to get Sara to leave the punk club earlier in the evening, talking to her during parts of the festivities when they knew that their past selves would be occupied, like in Back to the Future: Part II. This did not work nearly as well as they'd hoped, as they were almost immediately detected by the past version of Ava Sharpe who, ever the control freak, told the future Legends to knock it off and get back to their own time. She then went and got so drunk that she wouldn't remember seeing the future Legends, which indirectly explained Ava's uncharacteristic hangover in the season 6 premiere.
As Ava pointed out, mere mortals in the Arrowverse are at the mercy of causality, unless they are shielded by magic or a cosmic entity like the Speed Force. This means that it is all but impossible for a time-traveler to cross their own timeline and change something in their own past, due to the paradox caused by there no longer being a reason to go back in time to make the change in the first place. Even semi-professionals like the Legends have a hard time managing it, which is why they typically don't bother trying or do it behind the backs of the more responsible members of the team, who would object to their pulling the same shenanigans as Bill and Ted.
In the end, while the Legends probably could have engaged the ship that abducted Sara Lance in the Waverider, it wasn't worth the risk. As the events of "Back to the Finale: Part II" showed, it's impossible to anticipate most of the variables that can come into play with even a simple mission like getting a friend to leave a party early, without adding in the difficulties of attacking an alien ship with unknown weapons and defenses. Besides that, Legends of Tomorrow season 6 would be a great deal duller without the rescue mission to give it direction.