This is a core state function, with significant consequences. The article has an unpleasant reminder of this when it points out that the Auckland crown solicitor has giant blown-up newspaper articles celebrating death penalty cases on their office wall (which is... ick). While we don't have the death penalty anymore, these people are making decisions about who will face the might of the state and who won't, which laws will be enforced and against whom, according to guidelines of course, but the article points out that the lawyers are overwhelmingly white (unmentioned: also rich, and mostly male), meaning a centre of racism in the justice system. It also points out that the current funding structure creates incentives for quick plea bargains (and to dump cases that look too hard, meaning "too expensive"), meaning potentially unjust decisions being made.
And of course David Parker isn't going to fix any of it, any more than he plans to stop New Zealand being a financial fence for tax cheats. But he should. Prosecution is a core state function. And it should be performed by state employees subject to full state performance monitoring and oversight, including the OIA.
The optimum way to do this is by the government withdrawing the crown warrants and establishing an agency (or just an arm of Crown law) to handle prosecutions. But if they don't, then an MP who wants to change things could force that by bringing a member's bill deleting the mention of "Crown solicitor" from the definition of "Crown prosecutor". Alternatively, Graeme Edgeler has a bill to handle the OIA problem here.