We did not pierce our baby girl's ears. Human rights debates aside, there are some hygiene issues that I think deserve consideration.
I was allergic to nickel. Still am to an extent. But when I got my ears pierced at the age of 7, it was because I really wanted them to be pierced. That's why I was willing to put up with itching, weeping, swollen, hot, painful earlobes for years. I even used plastic posts and plastic sleeves on metal posts, which are bigger and hurt to put in. I was willing to subject myself to all sorts of torture because I wanted earrings that badly, but I cannot imagine subjecting a baby to that. Metal allergies are not uncommon, yet most people who pierce a baby's ears don't think of that.
Second, caring for pierced ears requires some attention to hygiene beyond all the myriad things you're already doing for your baby. My baby would not have put up with people touching her ears to clean them or rotate posts or examine them often to make sure they aren't infected. I love her to bits, but she's been stubborn since the day she was born. It's important to consider a baby's temperament when making a lot of parenting decisions, and if you feel that your child might not put up with the routine inspection and maintenance, I think it's advisable to wait.
Lastly, even children who are very afraid of needles can get their ears pierced. My sister is needle-phobic. We still managed to get her to do it, mostly because she was around 9 and still couldn't wear pretty earrings like her sister. She chickened out a few times but eventually got it done. The fear and pain can be overcome, even in the worst-case scenario with an extremely fearful child.