Does everyone in the group need to start the hike at the same time?
Yes. That way you know everyone showed up. That's called accountability. You have a name and a warm body in front of you.
If you are the group leader, you are responsible for everyone in your group. If you split your start times, you will have no idea when the others started. Although they tell you 5 or 6 am you don't know that because you had a 2 hour head start. You won't know if they even showed up! So you return from your hike and you are missing one or two hikers. Hopefully, they put a note on your car. That is if they could find it since there are a lot of cars at the trailhead and overflow parking.
Scenario 1: Your group and other other group pass each other on Hypoxic Highway. Your group is coming down and the others are going up. You finish your hike, your group is blowing the froth off a couple while chomping on a burger and fries and you decide to head to the hostel. You still have that other group out there. What is their status? Where are they? How are they.
Scenario 2: A ranger asks you for your permit and asks where are the other members of your party you better have a good answer. Rangers are not babysitters, but they are very concerned about everyone's safety. They are there to make sure everyone on that trail is in compliance and to assist if needed.
In another post, a hiker was missing and no one, even family, had no idea. You don't want this to happen with your group.
From the Sierra Wave: "Das set out to summit Mt. Whitney with a group of hikers on Sunday August 5th. After reaching Lone Pine Lake, Das became tired and stayed behind with one member of the hiking group to rest and nap. When Das woke up he was given instructions to go back down the trail and wait; at this point his other companion began to ascend the trail with the assumption that Das would head back to camp. At approximately 2:00pm Das was spotted at Trail Camp by the rest of the hiking group after they had summited Whitney and were descending the trail. Das refused to go back down the trail with the rest of his group and insisted upon summiting Whitney alone."
You don't want this.
For our hike on 07-25-12, I wanted to start at midnight. However, the group (wifey-pooh) didn't want to start until 2 am. Majority rules 6-1. We started at 1:40am with all present. We reached the summit, and I was sweep on the descent. It's not easy being sweep believe me. You have your pace, and the last person has theirs.
Safety first, last, and always.