The seafloor is quite deep in the middle, the currents and conditions are strong and treacherous, and there's an active fault line thrown in for good measure. This article does a good job of explaining the myriad issues:
https://www.rnz.co.nz/national/prog...2018631183/tunnel-vision-on-bridge-to-nowhere.
Now, this _is_ an alternate timeline, but I don't see where tech is advanced enough to make this physically possible by 2020, let alone 2001. There are some pretty hard limits on engineering projects like this and being ahead in areas like spaceflight won't really get you much progress on them unfortunately.
Also, I don't see how NZ would be different enough to justify it economically.
Thanks for asking 😃