I think the most important is that it takes some of the anxiety away for couples. I have never had a couple say they wish they didn't do it. Most report that it made them feel less anxious about the ceremony in front of big crowd. It gives the couple a few minutes to really share this moment, creating some of the best emotional expressions for the photographer to capture. Here is one of the groom crying and the bride is wiping his tear away.
We wouldn't have gotten that shot at the alter.
Brides say they still feel the excitement when the groom sees them walk down the aisle holding their dad's arm. Some of the other benefits are that most of the formal pictures can be done prior to the ceremony, so your guests don't have to wait so long for the bride and groom to join the party. Also the flowers and your make up are also still fresh for the pictures. I usually set it up somewhere when I am about done shooting Groom portraits and I have the bride come up from behind him and tap him on the shoulder and he then turns to see his bride for the first time. So fun!
Some brides choose to do a first glance with a parent instead. Here is one of a bride and her mom.
It also really helps to have 2 photographers to capture both parties. Here is one taken by my second shooter, Cynthia.
But ultimately it is a personal decision for each couple and I respect their wishes, if a first glance is not for you, that is perfectly fine too. There is no right or wrong, but a personal decision.