I feel like saying that Azrael's act of agreeing to reap Chloe's soul is a mystery, except maybe if it's another manipulation on Michael's part.
After Gabriel didn't support Lucifer in the voting, and Uriel who could like him ?
As for Remiel, she put her differences with Lucifer aside to do him a favour as a spy and at the risk of her life. Finally, Zadkiel supported Lucifer during the votes, even if he was reluctant at first. And he is funny too (dance scene with "Can't touch it".
So I understand why the majority prefer Remiel and Zadkiel.