More is not always better, especially when it comes to the amount of timber in the frame of a house. The more timber there is, the less space there is for insulation.
Most homes in Aotearoa are designed using the assumption that timber will make up around 14% - 18% of the area of a wall. A 2020 BRANZ research study found that in reality, the timber fraction is closer to an average of 40%. This means there is considerably less space available for insulation. Unfortunately, this is not always picked up during the consenting or pre-lining inspection process. H1 Energy Efficiency calculations are checked at the design stage, usually using the much lower default timber fraction assumption. The result of of all this is that many consumers are effectively getting less insulation than they're paying for, and much more thermal bridging.
https://www.branz.co.nz/pubs/research-reports/er53/
https://www.placemakers.co.nz/online/framology