First lets ask why would you want to form a cooperative in the first place? One reason is that it can deal with "hold-up" problems. Take as an example of a group of grain farmers who need the services of a miller. Let assume that the market for millers, at least in the beginning, is competitive so the farmers can tender out a contract for a miller's services at the competitive price. The contract is awarded to a given miller. Grain is delivered to him by the farmers but the miller refuses to carry out the contracted for services unless the contract is renegotiated. Let me make an additional assumption here that transportation prices are high so that the miller has, effectively, a local monopoly. The farmers clearly have a problem, their grain will rot if not processed. The miller can "hold-up" the farmers, that is, force a renegotiation of the contract so that its terms are more favourable to the miller. Cooperative ownership of the mill by the farmers is one answer to this problem since the farmers do not have an incentive to hold themselves up.
But does this kind of story make sense in banking? Why would producers, say farmers, want to own a bank? There has to be either high contracting costs or monopoly problems, as in my example, for cooperatives to make sense. The problem with this in banking is that there are a number of banks in a fairly competitive market so it's not clear to me what advantage the cooperative would have.
One advantage of a cooperative is their low ownership costs. Normally monitoring of the management of a cooperative is undertaken by informed members, say farmers. These farmers produce a limited range of outputs, wheat, wool, milk etc, about which they are very knowledgeable. Clearly this is not the case for farmers about banking. Further, collective decision making is normally helped by the fact that the interests of the members of a cooperative are very homogeneous. While this would be true for farmers of a given output it is not true with regard to farmers and banking. Farmers would have interests as heterogeneous as normal shareholders of a bank. So in this case it is not clear to me what advantages the cooperative has. And its not clear that there is any other group who could function better, than farmers, as members of a cooperative Kiwibank, given that the aim is to expand into the agriculture.
Another thing to note is that the example Homepaddock gives of a cooperative bank, Rabobank, is a cooperative of other banks. The following comes from the Rabobank website:
Although now a major international financial services institution, Rabobank has retained its cooperative structure, with approximately 161 independent Dutch banks as its members. True to its cooperative origins, the bank’s primary interest lies in providing the best service, value and expertise, and in establishing mutually beneficial relationships with its clients and the communities in which they operate.So the bank's members are other banks. I'm not sure if this is the form of cooperative that Homepaddock is really suggesting for Kiwibank, and if it is, you have to ask why would the other banks want to be involved in such a set up?
Or is Homepaddock suggesting that Kiwbank be turned into a cooperative owned by either producers, for example farmers as I have assumed above, or customers or workers. If so, which and why? As I said above it's not clear to me what the advantages of a cooperative would be in banking.