In the play Oedipus Rex by Sophocles, the question "is the truth about past events really necessary" is laced throughout the work, and the answer is left up to interpretation.
Oedipus lives greatly in his lie; he is the ruler of Thebes and is regarded highly. Once he discovers the truth that he killed his father and got his mother pregnant, however, he is unhappy and utterly destroyed. Decoding could not change Oedipus' past-- neither could his self-punishment, but he embarks on the mission because he wants to save Thebes. The sins he committed were not conscious decisions. He is bound by the oracle, and his actions do not reflect his character. If the actions had been intentional, then the guilt that he feels about the murder and impregnation would be more justified and deserved.
Oedipus was perfectly fine in his world of lies. To him, in fact it was truth. He believed that his reality was simply what he knew at the time (which did not include the killing of his father or the impregnating of his mother). After he seeks truth to save Thebes from the plague, he becomes unhappy. He conducts his own hunt for change after receiving advice from the oracle. The same quality that made him ruler also blinds him at the end of the play-- the need to find truth. The two situations (solving the riddle of the sphinx and finding the murderer) are parallel yet different in their benefits. Solving the Sphinx's riddle resulted in a positive outcome-- he became ruler and saved Thebes. Finding the murderer, however, was an attempt to save the city again but had negative results for Oedipus personally.
So should the truth be sought if the primary result is information regarding the past? We are presented the question but not the answer. Some may argue that the truth provides closure. Others might argue against that idea, saying closure is not needed, as nothing will change anyway. Pondering the question is left to us; and we can conclude, through the results of Oedipus' discovery, that being blind to the truth may be beneficial.