They had to surrender, if they didn't the war would be over and the Athenians would have won, let alone that Sparta had the most weird social system, and in the latter ancient years there was almost no real Spartan by their law... Anyway, Sparta won the war (and Athens never recovered) due to the Persians' support in money and navy, along with a great strategist of theirs and Alcibiades (a thorn in the Athenians side). If they had won, there probably would have been no Alexander the great as Athens would have owned Persia after that.