What happens when we get to the end of the Greek alphabet?
That's something for Gen Φ or Χ to worry about, sometime in the year 2420. If humanity makes it that far, it feels like a very minor concern.
More likely we just won't be using this archaic technology for generational cohorts by then, because we'll be using Esperanto or Universal Standard Hindi or Mandarin.
Reminder that esperanto is a bad IAL due to being based almost entirely on European languages, having a phoneme Inventory based off one of the languages Zamenhof happened to speak and having an agglutinative grammar that would be unfamiliar and difficult to many people
That is true, but it should be branded as such, not as an international language, localized auxillary languages can be great, see Interslavic as an example
They can switch to Cyrillic: az, buki, vedi, glagol', dobro... Then Futhark, and so on, there's no lack of alphabet systems out there. The preference for Greek is kind of lazy.