I had never heard of Alcibiades until I started reading Greek philosophy and even then he is only mentioned in passing.
This man who I think qualifies as the most interesting in history (from what I've read at least) seems to be cast as a traitor.
For one he is known to have saved Socrates in combat, is in Plato's Symposium, is a drunkard and genius (Tyrion?), sleeps with a Spartan Queen pissing off the Spartans, and is a major player in the Peloponnesian War: accused of defacing religious symbols in Athens just prior to the Syracuse campaign, pulled from the soon to be decimated Syracuse campaign, eventually killed by the Spartans in Asia Minor just before Athens major defeat at the Hellespont (due to oversight on Athens part), of which he actually commented on the events of just prior to it going down (unless that's just historical creative license). None of this mentioning his attempted comeback dealings on the island of Samos. This guy was truly epic. He died in his prime, unexpected (to him at least).
Yet, watching 300 we are to believe Themistocles a hero who eventually is ostracized and defected to Persia?
History is more complex than we initially give it credit for. Athens was vitriolic no, their ostracism is a complex mess of 'One minute your 'general', next your an outcast'? Power struggle 101.
My question is, why isn't Alcibiades more famous? Is it because of his questionable character? He seems to have 'Breaking Bad' written all over him.
Is he noteworthy? Is he not one of the most dynamic important character's in Greek history?
Dynamic yes, important no. That's probably the main reason why he doesn't feature in basic overviews of the Classical period. While he influenced many important events, his actions neither caused nor prevented the defeat of Athens in the Peloponnesian War. Given that his part in the events is extremely complex, it is generally easier to skip over him altogether than to try to explain in detail how one man's wild plans and repeated betrayals ultimately achieved very little.
The situation is similar with Alkibiades' contemporary, the Spartan king Agesilaos, whom most modern students will never have heard of either, even though he was admired throughout antiquity as a great leader and even considered the de facto king of Greece for a significant part of his life. In the end, he could not prevent the downfall of Sparta, and so he is now forever submerged in the wider flow of history.
That said, Alkibiades would certainly make a great character in a dramatisation of the Peloponnesian War. He's got either 'flawed hero' or 'charismatic villain' (depending on your point of view) written all over him. Plus, he was supposed to be really, really ridiculously good-looking.