In The Apology why did Socrates want the death penalty?
First of all, please realize that it is Socrates, not Plato, who is arguing that Socrates should be executed. I have changed your question to reflect that.
Basically, Socrates insisted on being executed because he thought that was the only choice he had if he did not want to betray his principles. He could have, for example, opted to be acquitted if he would give up his teaching, but he felt that his mission in life was to do just exactly that -- to go around teaching. Therefore, it would be better for him to die than to give up the mission that he had been given by the gods.
Socrates believed that what he was doing was important. He believed that it was important for him to go around goading people into doing right. He felt that this mission of his was so important that he was willing to die rather than to give it up. This is why he argued that he should be executed.
Actually, the question should not have been changed. Plato wrote a fictional speech which he put in the mouth of Socrates. This is not a verbatim transcription. The Platonic and Xenophonic accounts of the trial differ.
He could not have opted to be acquitted -- any more than a defendant in any other law court is given a choice of aquittal. Instead, as was standard Athenian legal procedure, after he was condemned, he was permitted to suggest an alternative penalty. This is not acquittal. Normally, he would have been expected to suggest the counter-penalty of exile, or a monetary penalty, which, for the reasons you state, he does not do. Instead, he suggests that he be supported for the rest of his life by the state, a suggestion that mocks the process of the trial. The counter-proposal is not accepted and he is therefore condemned to death.