Yes it is crazy at that time. And actually your plane won't take off for a while after you get away from the gate.
Due to the noise abatement rules in place for SNA the airlines ALL schedule the early morning flights very close together.
So you have about 20 flights leaving between 6:45 and 7. The airport actually "opens" at 7 so basically they load you up, line up and at 7 BOOM one after another flight after flight after flight
The result of this scheduling issue is that you have a LOT of people checking bags, going through security etc in a fairly short window. It can back up and crys of "I am going to miss my plane" won't really help as everyone is on the same schedule.