Wood told On the Tiles the original Northern Pathway plan that would have seen a new walking and cycling path clipped on to the existing Harbour Bridge had broad support, but the Government was told it was not technically feasible to go ahead with it.
The bridge was what officials recommended in its place.
"Clearly, it crossed a line in terms of public appetite in terms of cost: $360 million, people could bear; $680 million crossed a point where people didn't have a level of comfort with it," Wood said.
"I guess the best thing I can say about that is we listened pretty close for several months. The message was pretty clear we needed to do this in a different way that didn't cost so much. We heard that, we made the change."
He said options would be put forward to the public this year for the future of a new crossing for the harbour, but he had asked for trial options to be considered for the existing bridge.
Those options were coming soon, Wood said, but noted there were some complexities that needed to be worked through and it was "technically much more difficult" than people thought.
"If you do one lane, you'd have to put concrete median barriers along it. The weight of that on the clip-ons would create resilience issues. You'd have to take two lanes, so you'd start to get into a more difficult technical solution."
Asked if Aucklanders need to get used to congestion charges, Wood said they do and it has been signalled for a long time, with working going on over the past five years on it.
He said the rough estimate was that the charges could get peak travel times down to school holiday levels.
"The key thing for me is, I'm a Labour Minister, this is a Labour Government, is how you deliver that and how you keep equity in mind for people on low incomes.
"We have people in transport poverty, car ownership, which most people have to have, is extremely expensive, so how can we work through that and make sure it is fair for everyone."
On the podcast, Wood also talks about his early start in politics, potentially accidentally revealing the Government's elimination strategy for Covid-19 in a select committee meeting, public transport in the regions, and the state of the union movement.
• On the Tiles is available on iHeartRadio, Apple Podcasts, Spotify or wherever you get your podcasts.
• You can find more New Zealand Herald podcasts at nzherald.co.nz/podcasts or on iHeartRadio.