FairlieFlyer - the second direct flight (NZ38/39) was introduced only a few years ago (can't remember when, exactly, but definitely since 2000).
AFAIK it never went via SIN, though there were always options to change planes there (and at HKG) that could be quicker than the NZ1/2 via LAX.
It wouldn't surprise me if avoiding LAX was a factor in popularising the new route. Transiting in the US was never a bed of roses, even before 9/11
