On the Levellers Mission:
What we never really know is what the Levellers actual aim is. Some say to destroy humanity, others to keep population under control. My theory is that the Leveller is the Dark Gods warrior on the World, whose aim is to destroy all resistance to the Dark Gods domination of the World, possible by finding all the shards of Wyrd and destroying them, or reuniting the one dream so Wyrd can be slain for once and for all. Thus allowing the dark Gods to rule the world.
On the Cycle:
The cycle may have little to do with the actual job of the Leveller, or even the light/dark ages, but of the power of the Leveller.
The cycle's always heralded by two things, Tharsis and the Comet, these may be connected to the Leveller's and the Hero's power.
Tharsis may be the conduit to the Dark Gods and thus the souce of the Levellers power.
The Comet may be the source of the Hero's power, a conduit to the Light Gods, If there are any.
Myth III clearly defines (and Myth I and II also suggest) the before Tireces it was always Dark. Thus it was not unusual for the light to win several times in a row, the Leveller had done it before in the Axe Age, the Light had done it against Moagim. Only Moagim had a backup plan, Balor was far too sure of himself and had no back up plan. This links to my other Theory about the SB Watcher relationship.
Thus the cycle may not be broken, it depends on whether or not the Leveller is truly dead, even if he is, it is possible that some powerful dark mage may try to harness the power of the Dark Gods.
On the Levellers' attempts to win:
Many say that Mjarin was particulary un-Levellerish, however perhaps he was just trying a different angle:
Sorangnath:May have intended to rule the world first then take the dreams, but his power weakened too much before he could complete his domination.
Moagim tried to destroy the light resistance by killing it off and then going for the dreams, and when that failed, getting it eaten by the Myrks, knowing that when the next Leveller came humanity would be far weaker and the Levellers mission could be completed.
Mjarin:He tried to take over from within, setting up Moagim Reborn so he could take control as the valiant hero and killer of the Leveller (well no one would know better), destroy all the non human Light nations, or those a threat to the Leveller, then do what he had to do, an angle that also nearly succeeded.
Balor:Balor followed Moagims style, kill them, all of them. He too failed, barely.
SB: (Yes I know he wasn't the Leveller but may have wanted ot have a stab at it anyway, he was pyscho after all.) Tried to do it by killing everyone, first the ordinary way, then by blowing up Tharsis, however he would have kept it as a last resort becuase he knew that it was the conduit to the Dark Gods, the risk being that he may kill everyone, only to have destroyed the Dark Gods only access to this world.