That is true but it would be difficult to find what you were looking for if it happened a few days earlier. If there was a way to search for people on the logs such as looking for a specific name on the kicked section then it could be very useful and easy to use. However I don't know how much work it would take.
It would likely take a lot of work, unfortunately ;P
The gang leader don't always have to look at it, its just as a reference. Let's say a member was randomly kicked and asks why, the leader then can check who kicked him. This could end the idea of members blaming eachother