I would like to be able to assign new member approval to a moderator level user without the need to grant them full admin control-panel access.

In our case this could be a task easily delegated to certain people who I would prefer not have access to all the control-panel configuration options.

Abbott

You would think under CP Permissions > Can edit users > Moderators set to 1 would enable them to approve users.

I would say give it a try.

It doesn't sadly.. But you do have a point, you'd think it would or there would be an option for that...