Like [MENTION=10582]brinkster130[/MENTION] said, we know that humans weren't meant to handle the visions and that only someone who was at least part demon could endure them without suffering.
Furthermore, I think it may be part of the tests and trials given to Cordelia. We know from the finale of Ats season 3 that the PTB were testing Cordy throughout, and it's possible that they could have amped the amount of suffering that the visions caused her in order to determine whether she'd be willing to give them up. Refusing to give up her position as "vision girl" is probably the first thing that alerted the PTB to the possibility that Cordy had what it took to be a "higher being." (That was so incredible of her, btw).