And it seems to have worked, to a degree. Over 2,000 years later, everyone from layman to politician invokes his name and death as often as they do Jesus. Not existing is often a really good way of kind of existing seemingly forever.
He chose to remain faithful to speaking truth (or what he believed to be true and asking questions to humbly discover it) rather than acquiesce to a bunch of manipulative tyrants. Such actions not only commit you to stand by the truth in thought, word, and deed, but they inspire others to do the same and thus disperse the evil of the world. It was a blow to the systemic lies of myth and sophistry employed by the powerful of the world.
Socrates did not choose death. He chose truth while accepting that he would be killed by those in power. Big difference, except for a utilitarian.
Now whether he should have chosen exile, I don't know. In some sense, what he chose is heroic and more inspiring than skipping town. Christian martyrdom is like this. A Christian remains steadfast in the truth even to the point of death. This is a faithfulness to Truth that cannot be destroyed by evil men who would use fear to part us from the truth and toss us back into the darkness and slavery of lies. In remaining faithful to the truth, the martyr truly lives and is truly happy no matter what pain comes his way, whereas some men spend decades rotting in the misery of lies. The martyr loves the truth to the point of the extinction of self. He also dies in anticipation of the Beatific Vision. This is the greatest fulfillment of a rational being wherein the doors of the soul are flung open to the infinite fullness of truth. In the vanity of the City of Man, on the other hand, men love themselves to the point of the extinction of truth and thus live in death and misery.
The truth will set you free and so in a sense Socrates died as free of a man as you might have reasonably expected a pagan to be in his position.
If people still read the Classics, this would be widely known as table-stakes.
No, he was an actual historical person. Plato of course wrote a more literary depiction of him, not a direct transcript of his conversations.
> If Socrates was so wise, why did he get himself killed in such a dumb way?
You should probably actually read the dialogues (at least the Apology and the Crito) and you'll understand what happened. Socrates explicitly chose not to escape prison and to go through with the execution, and he gives his reasons in the Crito.
The smart way to die?
Maybe he was on the autism spectrum?