I still don't have any problems with Starchild. Starchild was always meant to be stupid and inconsistent with the logic presented to us. It was designed by an apex race too stupid to realize their own mortality. When something stupid creates something, you can guarantee it to be stupid. The AI was built using the knowledge the Leviathan's had of their own cycle, and there's no way the Leviathan's would have been able to predict how every single cycle was going to operate because they couldn't see past their own. That's why I have no problem with the Starchild to be honest, because it best represents what happens when AI is designed poorly. Not even showing the AI evidence to prove it wrong wouldn't compute with the AI because it's creators couldn't compute that they were wrong about anything. A lot of the series has been about stopping villains too stupid to see the failure of their logic. It's thematically consistent.
I really don't want to make this into yet another ending discussion but you are describing a VI, not an AI.
It's a mistake that most SF writers make at some point. A true artificial intelligence would be just as flexible and capable of learning as any of us (if not more so). EDI is portrayed pretty well in that regard (even though she overdoes it on the "I am truly alive now" phrase). She is capable of of not only taking facts and processing them according to her original programming but she is able to learn, extrapolate and change her own ideas and preconceptions.
That is what is supposed to set her apart from, say, Avina. Any artificial intelligence would be able to that, otherwise, it's not an AI.
The catalyst, according to the Leviathans and himself, is the most sophisticated AI there is and yet, it acts like a VI.
And - to get back on topic - if travel to other galaxies is a possibility, he is even more confined than we all thought because he cannot even extrapolate his pre-programmed premise to a universe that includes more than the milky way, making his arguments all completely pointless.
EDIT: Plus, what PinkysPain said. All indications are that the writers wanted the ending to be highly intellectual and philosophical. If in the final analysis, the only explanation of the facts is that the catalyst was just stupid, then I'd say they failed rather spectacularly.