Musicians do not like them. They sell well, so they get invited back (much to the disdain of the musicians). After this dust-up, maybe this will change.
Remember Kathleen Battle? Everyone HATES her because she is a snobby diva. One orchestra hated her so much that when her concerts were over, they wore "I Survived The Battle" t-shirts!
I have a DVD of Don Giovanni with Battle as Zerlina. While I'm very aware of her outrageuos behavior, I've always considered her quite the hottie...