Groups are a system-wide resource that are stored in a single file owned by root. The current group format makes no distinction between "user" and "system" groups other than GID range, and even if it did, it has no way of granting access to portions of the file to different people. Because of this, you would have to come up with a new system to allow non-administrators to add and remove groups without giving full access via sudo and equivalents. There apparently hasn't been enough demand for this feature (likely because Unix installations were originally institutional), but there was enough demand to implement a related feature.
You can delegate a user to be able to modify group membership using gpasswd. If you give a user administrative control over a group, they can then add or remove members without having to have root access (by default, there is no group administrator, so only root can make changes.) Given the following (as root):
# groupadd newgroup # gpasswd -A owner -M member1,member2 newgroup
The user owner can now modify the group newgroup without having to get any other permissions:
$ gpasswd -a member3 newgroup Adding user member3 to group newgroup
(You'll notice that the group administrator doesn't actually have to be a member.)