Most would probably agree that it was a good idea for New Zealand to appoint a Chief Science Advisor back in 2009, and that doing so has raised awareness of the way of science stimulates innovation, which in turn is the potential source of many benefits. But science policy in general is rather less loved, judging by a recent survey of scientists. Here, for example, is the summary of responses to question 3.
I guess the idea of "National Science Challenges" stemmed from the popularity of innovation competitions generally, which sometimes amount to outsourcing an R&D task (as Netflix did) and other times aim to promote entrepreneurship generally such as the Spark competition at the University of Auckland. Maybe if you surveyed everyone who entered those competitions you might also find lots of people were not terribly gruntled and a few (the winners) who loved it.
But the nature of science adds a couple of extra dimensions here.
First, as Stephan's essay on the economics of science notes(pdf), the normal practice of science is a highly competitive, winner takes all affair. The imperative of getting "there" first is strong enough to make scientists secretive, possessive, perhaps even jealous and devious in their dealings with "colleagues". Participating in another winner-takes-all competition might not be too thrilling against that backdrop.
Second, while these people are highly skilled professionals, their job security in New Zealand is not great. Unless the research funds continue to flow, the job might not last long. And they're vulnerable to idiosyncratic decisions like the closing of Invermay. In that context, the funds on offer in these science challenges might look more like desperately needed resources than some cool extra fun.
In normal markets, competition doesn't always stimulate innovation: if it is too intense, there is no money to pay for R&D; and if it's absent there is no need to bother. So innovation doesn't happen so much at those extremes. I suspect something similar might apply to science in NZ, with the best way to promote scientific innovation requiring more of a balance between job security and competition.