While a hero, Yi as a person and his naval campaign are a lot more nuanced than what is commonly taught.

Yi Sun Sin actually had a huge fleet in comparison to the Japanese during the first invasion, because not only he had his own fleet, he was also joined by Won Gyun's fleet and Yi Eokgi's fleet. Most of his campaign should be properly recognized as a joint operation of several Joseon fleets led by several admirals of equal rank.

(Dispite what Jingbirok claimed about Won Gyun, he actually spent the majority of the time during the First Invasion fighting the Japanese together with Yi—political slandering and character assassination at the time went both ways. Yi Sun-sin's exoneration as a hero comes at the expense of Won Gyun's reputation).

Yi's naval campaign also wasn't just a string of victories after victories. He actually had his share of defeats, especially towards the later part of the First Invasion after Japanese adapted to his tactics. There is even one case of Yi making false report claiming victory yet vented frustration in his personal diary.

Yi's lack of results during the later part of First Invasion contributed to Joseon king/court losing patience with him. The so-called "double agent plot" was only the last straw broke the camel's back, and the "double agent" part was almost certainly just a face-saving excuse. Japanese invaders at the time barely knew any Korean language, there's no way they could understand the intricasies of Joseon court politics to pull off such trick. It's far more likely that Konishi Yukinaga GENUINELY wanted to backstab Kato Kiyomasa through Korean hands, as he later tried it again (and almost succeed) during the negotiation.

Likewise, Battle of Myeongang was indeed legendary, but in the end Japanese still had hundres of ship, while Yi only had 13. What happened after the battle wasn't pretty. Also, Japanese had 130 ships, not 300.

Also, Battle of Noryang was led by Ming admiral Chen Lin. Yi advised him and controlled the Korean part of the coalition fleet, but Chen Lin was the commander and had the final authority , so credit/merit should be his.