a lot of the NY owners seem to claim you have to be....
As for the original question, there are a couple of reasons you don't see very many Z's that go fast in the quarter mile.
There is a pretty large contingent of Z owners that have no interest in anything time-competitive. It is a gorgeous car, and so there are a lot of people that enjoy it as a head-turning, and spend their weekends detailing them rather than tracking.
Then there's a pretty large contingent that enjoys bench-racing rather than actually running their cars for times. Look no further than
this thread to see tons of speculation with very little backup for their times. Inflated dyno numbers are easy to get, track times that back them up are more difficult.
The Nissan crowd also tends to love running hellaflushed setups with 5000 degrees of camber, which tends to set people up for running 6 second 60' times. Things like stiff rear springs also don't really help getting weight on the rear axle either.
The 350 suffers from a lot of these issues as well, but the power distribution tends to make it a little bit easier to run down the quarter mile, especially the peakier torque curve. The VQ37 lays down an amazingly flat curve, sometimes it makes it a little tough for some people to get it down the track.