The whole business of how the AI votes in the GC is pretty opaque to be honest, with essentially nothing explained in-game. There is a bit more logic to it though if you look at the files, although we can certainly question some of the numbers.
GC votes aren't decided by the usual additive "reasons to accept" formula you see in bilateral diplomacy. Instead the game uses the multiplicative "weight" system, which Paradox usually uses for probabilities of random occurrences, but in this case it's used to make deterministic decisions according to certain thresholds. There's a base weight depending on the resolution, which ranges from 3 "hated" to 7 "loved", but most resolutions have a base weight of 6 "normal"; the threshold weight to vote yes is 7. A weight of 10 is enough to make the AI call an emergency resolution.
Some factors are a hard no (weight 0), for instance on repealing ideologically aligned resolutions. Aside from those "veto" weights, though, the weights for things like ideology (which you'd think would be pretty decisive for some resolutions, like the Greater Good line) are in the range 0.5-2 and often more like 0.8-1.2. The weight for the opinion of the proposer ranges from 0.5 to 1.3.
Looking at the weights for the endgame crisis resolutions, having the crisis empire literally neighbouring you is only a factor of 2, so only enough to cancel out the weight of hating the proposer. You only start getting a positive weight for crisis progression at stage 3, and even then it's only 1.25; for reference, stage 3 means the Sentinels have appeared against the Prethoryn, or the Aberrant have arrived, or the Contingency holds 20% of the galaxy. There are also some ethics factors, but they're pretty small as well. The overwhelming weights only kick in when the crisis reaches crisis stage 4, which is when much of the galaxy has been destroyed, as BlackholePD observed.
Contrast with denouncing a "become the crisis" empire, which has a base weight of 4 "disliked", but gets a couple of hefty weights of 5 each once you reach 1000 and 2000 menace (the first only if the AI is inferior to the crisis empire, the second for everyone). So indeed, the GC is much more likely to respond to such empires than it does the Prethoryn and so on.