To provide a little more detail than I could fit in the title:
To start off, I am aware of the tyrants, but that was a very different institution and they were not conceptualized as "kings"--in fact you could say the very definition of "tyrant" was non-regal one man rule. I also know there are a couple exceptions like Macedon, but they are really just barbarians anyway.
My question really came about with a comparison to Rome. In Roman mytho-history, there is a very clear narrative of heroic foundation followed by kingly rule, then overthrow of the kings followed by oligarchic rule with some institutional survivals. The Greeks cities as well follow many of these parts--they posses narratives of heroic foundations and kingly rule, and in historical times oligarchic rule with some institutional survivals, but none have a story of the overthrow of a king. I would love to be wrong on this point, but I have scoured Fowler, Gantz and other sources and found nothing. Just a general acknowledgement that, say, Thebes was once ruled by kings, and now it isn't, and no explanation of how one became the other.
So my question is twofold:
What happened to the titulature and institution of wanax and basileus? I assume something involving the social churn of end of the Mycenean period, but they seem to have left a very strong memory (and their appearance in Homer is striking, particularly if you follow Finley's argument that Homer is a description of Dark Age society).
Why do no Greek authors record the end of kingly rule? Why does this not become embedded into the common heritage of Greek poleis? It's maddening.
This is a really tough question to answer, and I certainly can't "answer" it, but I can contribute a little to your thought process.
Regarding #1: the central authority figures of the LBA Mycenaeans (wanax or basileus or whatever) are these days assumed to have wholly disappeared with the collapse of the palatial system. Some of their basic behaviors persisted (more on that later), but nowhere in "Dark Age" Greece do we find compelling evidence pointing to anything but emerging oligarchic structures based on kin (or perhaps regional) groups. If you read up on "Dark Age" Greece you will hear a lot of talk about "Big Men" and Sahlin's comparative work on the theory of social organization around "Big Men." The classic case is the individual buried under the late 10th century monumental structure at Lefkandi. Its discovery (in the 1960s I believe) has certainly altered the consensus on what "Dark Age" Greece was like, but even this great example does not seem to be any sort of continuation of a Mycenaean centralized authority. He is, more likely, very similar to a very early Greek tyrant: a participant in a narrow oligarchic structure that, by whatever means, came to out-compete his peers in the accumulation of prestige. I think most these days would argue that the societal structures that emerged in the ruins of the Mycenaean civilization were very different from what came before, and were unequivocally based on narrow elite groups. What it took to assert elite status changed as you move from the 10th to the end of the 8th century and beyond: "warrior graves" with metal objects/weapons eventually give way to association with land tenure (especially in Attica, the Corinthia, the Argolid, Boeotia, and Euboea) and prestige display in pan-Hellenic sanctuaries. Gift exchange, reciprocal exchange, or whatever the French are calling it now -- this seems to have been a basic LBA mode for asserting and maintaining prestige among authority peers, and in particular unequal or re-distributive exchange. The go-to for that topic is Alain Duplouy. I think it is a very big mistake to assume local Homeric "kings" holding court in the Geometric period. Virtually all the evidence points to prestige competition, which is for me the smoking gun of fundamentally oligarchic structures.
For #2, I can't think of a single example either. We should probably only expect to find literary references to the transition in Athens, since the vast majority of the sources are Atheno-centric. The Orestaia cycle of Aeschylos deals with some of the themes of transitioning to a demos-driven government, especially Eumenides. That might bear some fruit, but it is pretty tangled up in its mythic setting and its 5th century Athenian political context. The Athenaion Politeia probably had something to say about it, if that section had survived. Plutarch seems to know something about it when writing Theseus but he just says "Theseus first pandered to the demos, as Aristotle says, and turned over his rule to them, as even Homer seems to support, when he applies the term 'people' in his catalogue of ships to the Athenians only." Not much to go on.
Maybe the Romans preserved more narrative on this topic because the kingship had been particularly traumatic and undesirable. It would follow then that memory of the removal of that trauma would be stronger. Perhaps the Greek sources just did not find the transition to be interesting or momentous? That seems like a lame line to pursue, especially since the Athenians were so preoccupied with the transition from the Peisistratids to democracy.