I just did this today at Long Beach. Was kinda confused that a class D had it but we used it. I made my call, and the guy simply told me to contact ground. I did that and repeated the same thing I said to Clc Del, then was allowed to Taxi a few hundred feet to talk to tower and off I went.
I don't really see the point of clearance delivery at some of these airports.
Maybe its an outlet for lonely controllers?
I suppose with the amount of 121 traffic at LGB it can clog up the grn freq though.