Obviously not NOW. In the future, when Korinth isn't a problem and the gratitude has faded.
I mean, sure, eventually, given time. We wont remain prominent forever. Eventually even Rome stopped being the capital city, and Mediolaunum, or Ravenna took over that role. Eventually Byzantion turns into Constantinople, City of the Worlds Desire. Eventually Sparta turns into nothing more than some lonely columns and overturned stones.
If Nea Kymai ever eclipses us, it will not be within the time frame relevant to this quest. But nothing they can do right now, in the near or even distant future of this quest, is able to threaten us or our position.
The whole problem with the far future is that it's difficult to predict what problems or disagreements will come up. The good way to plan for the far future is to limit actual vulnerabilities and not rely on unchanging motives, or floaty ideas like gratitude. I don't believe that spreading the Divine Marriage to Kymai is the sort of 100% slam dunk guarantee of besties forever that everyone seems to be claiming it is. One thing humans are great at is finding reasons to fight.
Gratitude is nice, but it eventually fades. But that is not our goal.
Our goal is to have similar interests, and to make servitude to our league more palatable by making their practices in commonality with our own. By having similar interests, and things that they can lose if they leave, it makes them unwilling to actually leave or move towards that goal. There is nothing that they can gain from leaving the league that they cannot gain within it, and much to lose besides.
By being generous, by showing them that in order to gain what they want, they must give us what we want, we bind them to us and make them unwilling to leave. The only thing Korinth has to offer them is their lives, and the only lever Korinth has to apply to them is the tip of the spear. But in such a situation there is more for us to worry about. This goes on until they can only imagine their existence as one in the context of their presence within the league. Korinth has nothing to offer them as temptation, and so the only thing left to Korinth is the way of force.
But we are also fostering a relationship with Athens, who we can use, for now, as a counterweight to Korinthian ambitions. While we might be unable to fight Korinth, Athens is very able to fight Korinth.
If you are going to talk about Nea Kymai leaving, something has to change in our relationship in order for such an event to be possible. Simply giving them the Sybil is not enough to plant the seed of competition or secession. There has to be a specific
reason for them to want to go it on their own, for them to be
able to go it on their own. Simply having the Sybil is not enough, as the Samnites and Oscans have demonstrated.
They need numbers, which they wont have as they have refused the Linean Laws. They need money, and it will take time for them to set up. They need allies, which they wont have except through the league and what we organize on their behalf.