*Lost Storyline from Ultimania - Described by the Compendium*
The story above may not be the plot as originally intended for Chrono Cross. Signs point to another overaching storyline that involved Serge binding with the Time Devourer itself; in this scenario, Serge, if he did not defeat the Time Devourer with the Chrono Cross, would ultimately bind with it and cause the Devourer to mature, granting him the power to consume space-time. Chrono Cross Ultimania mainly supports this notion, claiming that the Arbiter of the Frozen Flame must mediate between his fellow lifeforms and Lavos, or else he will inevitably bind with the creature and spell destruction for other humans. Ultimania also postulates that Schala was an Arbiter of the Frozen Flame while it existed in Zeal, and that is how she came to bind with Lavos. Apparently, the Time Devourer needed enough power before it could reach maturity, and Serge would have been the final piece in the puzzle. Quotes in the game also seem to hint at this possibility; three come to mind specifically. A demi-human in Marbule states that "anyone who touches that Flame will become a different being." Lynx, at Viper Manor, warns Serge that "there shall be a deep enmity between you and the world" once destruction occurs. Lastly, Belthasar notes that the Arbiter will gain "extraodinary powers...by binding with the new seed of destruction, the Devourer of Time." However, this storyline is not directly stated or implied in Chrono Cross, and neither has series creator Masato Kato confirmed it himself. For the time being, it remains speculation made by the Ultimania authors. Considering that in the same book, they contradict other canon (such as stating the Prometheus Circuit is not Robo, when Masato Kato noted that the circuit is Robo), the veracity of Ultimania is arguable.
Spoilers for Xenogears
Okay, this is why I think the interpretation of the story is correct. For those who have played Xenogears, you should have noticed many similarities to the plots of Chrono Trigger and Chrono Cross. I think all three games were developed by the same team, and Masato Kato even wrote the script for Xenogears. In Xenogears, there is a being named Deus, who is very similar to Lavos. Both landed on a planet and "created" humans and used human evolution to their advantage. What I'm about to explain fits more appropriately with the Time Devourer, though. According to Ultimania, the TD needs to bind with Schala and Serge to complete it's development. Only then would it become a complete Time Devourer. The TD already has Schala, it just needs Serge since he is the Arbiter of the Frozen Flame. He became the Arbiter when he made contact with it, and he's been granted special powers directly from Lavos. Serge is the final piece the TD needs to devour all space-time. Also, Kid was created when Schala heard the cries of Serge across time. Kid was a part of Schala, and her purpose was to guide Serge in his quest to destroy the TD and liberate Schala. And when Lavos landed on the planet, the Frozen Flame was separated from it. This is a magical object that is considered to be the ultimate treasure, and is vital to the TD's development.
Now for Xenogears. Fei/Abel is known as the Contact because he made contact with the Zohar, an engine that contained the Wave Existence. The WE was essentially God, thus the Zohar contained a god-like power. The Zohar is similar to the Frozen Flame. It is the most powerful object in our universe. The WE wished to break free of its confinement, so when Abel made contact with the Zohar, the WE granted its power to Abel, and since Abel was a child and desired his mother, the WE created Elly to be Abel's mother-figure and placed its will into her. With the WE's will, Elly's purpose was to guide Abel and all of his incarnations in his quest to destroy Deus and liberate the WE. Now, Deus needs the best humans possible to complete its restoration process. Humans are "parts" for Deus. However, it also needs the Contact (Fei) and the Antitype (Elly), to regain the power of the WE, which is contained within the Zohar and is the source of its power. The Zohar and other vital parts of Deus were separated from it when it fell onto the planet, and it must retrieve these parts. Deus binds with Elly, the will of the WE. To complete its resurrection, it needs to bind with the Contact (Fei). The Contact contains the power of the WE, making the Contact something like a god. If the Contact is binded with Deus, Deus will evolve into its full potential and leave the planet to fulfill it true mission (which isn't important here, and is a mystery anyway).
Both Serge and Fei, as Arbiter and Contact, destroy the Time Devourer/Deus with the guidance of Kid/Elly (the will of Schala/Wave Existence) and liberate Schala/Wave Existence. Schala was a part of the Time Devourer, and the Wave Existence was a part of Deus, and both sought to liberate themselves from their captors. Both had help too. Belthasar orchestrated Schala's liberation. Karellen orchestrated the Wave Existence's liberation. Yet, they had very different agendas. Belthasar's ideals were noble. Karellen's ideals were misguided.
And one more interesting similarity. The Contact and Antitype were destined to reincarnate until Deus was destroyed. Every time they meet though, they don't realize who they are and don't recognize each other. In the ambiguous ending of Chrono Cross, it is suggested that Serge and Schala will reincarnate in different time periods until they find each other, yet they may not recognize each other.
Then there is the theme of overcoming God. It's more obvious in Xenogears, but the Chrono series depicts Lavos as a god that humans must reject. The triumph of humanism over theism.
So this is why I think the Lost Storyline of Chrono Cross is the true interpretation. What are your thoughts on this subject?