having a new critter in the game is a step forward. These behaviors for it are two steps backward. However, we can keep the baby when we toss this gross bathwater, and get something cool later.
I think it could be improved if they make the following (admittedly unlikely) changes:
1. It becomes a neutral mob like wolves, zombie pigmen, polar bears without cubs, and endermen you don't look at.
2. It naturally hunts spiders... or zombies. Spiders and zombies don't have any natural predators, whereas wolves attack skeletons and creepers are terrified of cats. The idea of it only being out at night (to hunt) would be cool, and attracting them with big piles of rotten flesh or spider eyes would be a neat mechanic.
3. They should just be 'around' in the sky. Not necessarily only triggered by certain events. Relatively low spawn chance that's always active.
4. They should drop something COOL to incentivize hunting them! For instance, what if Elytra were to have come from THEM???
Alternative on 2: what if they were predators of endermen, and were actually native to the end, only popping into the overworld at night to follow some of the endermen that come here and feed upon them. In the end, they would be plentiful and glide peacefully through the void preying on endermen... shulkers could view them as hostile and their 'levitation' projectiles have the opposite effect on them, making them drop out of the sky, take fall damage, and be helpless on the ground for a bit, which gives a neat little reciprocating ecosystem to the end.
In the case of 4, they currently drop Leather, which is likely a placeholder until they figure out how to make a good drop for them. Since you mentioned Elytra, they could drop some sort of means of upgrading or repairing Elytra (In the latter, it replaces Leather itself), such as "Phantom Hides" that can additionally be used to create other vehicles.
As for the alternative to 2, they already also spawn in the End, so that would be fitting.
As for 1, they could simply spawn, but only attack the Player if the latter hasn't slept enough.