Because the others wouldn't have benefited in the same way.
Glenn would not have profited from going back and saving Cyrus from death, because his problem wasn't that Cyrus died. His problem was that he always lacked the confidence in himself that he needed. He needed to find peace after the fact in order to give himself the strength to be a hero.
Marle could possibly have benefited from it, but she matured because she realized that the Chancellor had been lying about her mother. Had she been able to witness the events herself, or prevented them, she would have been deprived of that maturity and trust of her father.
Crono's father isn't even a concrete point. We don't know anything about him. Some people think that he's dead/divorced/MIA/Dalton/on a business trip, and that caused Crono to train and be buff. On the other hand, Son Goku could have just flew in and had a one-night stand with Gina. Moot point.
On another point, you could say that this was the only possible way in which Lucca could find peace. Glenn was able to find his in Cyrus's blessing and forgiveness. Marle in her relationship with her father. And Crono in whatever the hell he was doing. Lucca didn't have that luxury.
BTW, even if Lara doesn't lose her legs, Lucca's journal states that she still had a passion for technology after the incident.
