AirNZ additional baggage is extremely cheap, so that may still be a factor. Not been through LAX in cattle class myself, but all those I've spoken to recently didn't seem to have as much of an issue as some of the above posts would imply. Having stayed in the lounge despite being in Business on the way back from the recce then I didn't think it was that bad. Also I found the security staff very helpfull when I needed to be full screened and was on a very tight turnaround.
So it takes all sorts, but my personal experience, and that of my wife was that the myths are worse than the reality of LAX.