The point of this fictitious debate is that the development of constitutional law has very little to do with the formal US constitution. Over the past 50 years, the US Supreme Court has invoked the US constitution in ruling on the legitimacy of abortion, the death penalty, affirmative action, political campaign donations, and various other matters. They are not expressly covered by the constitution's text. Rather, general constitutional provisions describing such matters of freedom of speech and cruel and unusual punishment are applied to specific situations. Constitutional questions are not resolved in an ether.
Put aside for a moment whether it is best to have unelected judges, rather than an elected legislature, determine the law on such issues. To properly understand the US constitution, we need to read not a single document, but a large number of Supreme Court opinions, consider various conventions of judicial and legislative practice, and understand presidential administration behaviours. In short, we need to understand an extensive unwritten constitution.
An interested member of the public wanting to properly understand the US constitution, its arrangements, its law, and how it works in practice, in an easily accessible format, would most usefully turn to a textbook. We can do the same with the New Zealand constitution.
If Palmer and Butler's main goal is accessibility, and public understanding of the constitution, they could as usefully advocate for more teaching of civics in schools (something Palmer has suggested elsewhere, in law review articles), they could disseminate media on constitutional issues (something Palmer has done elsewhere, via National Radio), or they could publish a new book.
What they don't need to do is promote a New Zealand Constitution in the sense of a single written document of four, 40, or 400 pages. It won't make our constitutional law more accessible. It might even expand the unwritten constitution, through cases interpreting this new document.
Some of us quite like a system that means issues like abortion, the death penalty, affirmative action, political campaign donations, and yes, even gun rights, can be decided by an elected Parliament, not unelected judges.
The irony is that in suggesting something that is unwanted and unwarranted, Palmer and Butler are drawing public attention to the benefits of our current constitutional arrangements.