The tunnel would run from north of the Terrace to Wellington Road.
This would be amazing for anyone heading out to the bays or Wellington Airport, no intersections or lights to worry about, and it would make life so much easier for the CBD as well, not having so much through traffic in the CBD.
I mean, we've got no shortage of tunnels in Wellington, many of which have been around for over a hundred years, and withstood many earthquakes already. Building a quake resilient tunnel can definitely be done.
So there's 3 tunnels that we run vehicles through, day to day (that im aware of). Terrace tunnel, mt Vic and the bus tunnel. The city would struggle with either of them collapsing, and I understand the ones under mt Vic are already in dire straits, going by some of the points hopeful mayors that they were campaigning on. I'm no expert but your claim feels like a huge stretch.
As for earthquakes, there's one that was readily found via a search in 1855 and that "considerably reshaped the geography", so, respectfully, I completely disagree. https://www.wcl.govt.nz/heritage/earthquakes.html
edit sorry, I should have clarified earlier, it's the major quakes I'm concerned about. Not the frequent little ones