A sensible person would expect both the politicians and the central bankers to be at one in getting on top of an issue which also carries significant systemic financial risk.
But governor Graeme Wheeler's failure to use the weapons in the bank's arsenal is not helping.
It has created a vacuum which speculators will now leverage ahead of the bank's "potential introduction" of tighter loan-to-value ratios later this year.
Key and Wheeler should realise it is pointless to carry on with what is starting to look like a political version of the prisoners' dilemma.
Neither appears to want to be the first to move with new measures.
Is this because each side fears they will be judged on whether their preferred measures actually work? Or is it because they fear being the first to move will be seen as an admission that their previous policies have not slowed the housing boom?
It is a full-on absurdity.
Key criticises the central bank for floating the "potential introduction" of tighter loan-to-value ratios for investors - then doing nothing.
He has also chivvied the bank over the proposed debt-to-income ratios.
For its part, the bank - via deputy governor Grant Spencer - says the Government should curb immigration and ensure housing supply is increased; a step that requires both central government and the Auckland Council to actually make some bold moves.
Key was criticised for delivering the Reserve Bank a "just get on with it" message ahead of Spencer's housing speech this week.
It was widely seen as blame-shifting.
When Wheeler recently fronted a parliamentary select committee meeting, he pointed out that in Auckland, investors accounted for 46 per cent of residential housing transactions.
"It's providing a lot of impetus in the market," said Wheeler. "So that's one area we're looking at around the LVR [loan to value ratios] around investor activity ... we're still doing the analysis."
He said these controls could be introduced before the end of the year while debt-to-income limits were some time off.
But with the continued rate of acceleration in Auckland property prices, such statements - unaccompanied by action - are simply an invitation to speculative property investors to pile in before the banks limit their access to credit.
Scuttlebutt suggests trading bank chief executives are waiting for the Reserve Bank to tighten the ratios, fearing that any bank which takes steps ahead of the central bank will lose clients to competitors.
There is some force to this argument. The Chinese banks have recently targeted offshore property investors after the Australian trading banks declined to service them.
Key's stratagems are obvious. But what this affair does do is focus attention on Wheeler.
Prime ministers have goaded central bank governors before.
But usually they hit back.
Given Wheeler's silence, it has to be debatable whether he will put up his hand for another term as governor.
He was a forceful figure when he first arrived on the scene fresh from a lengthy stint at the World Bank. He has had a stellar career, including at the NZ Treasury. But Wheeler's profile has significantly diminished this year.
It is notable that he has made only one formal speech in 2016. He holds OCR press conferences and has a preference to brief select journalists off-record.
But on this major issue, Spencer makes all the running.
Yesterday, Key was due to meet with Auckland Mayor Len Brown. The Unitary Plan is due to be reported back soon.
The Government has signalled that it will appoint a commissioner in Auckland and set up an Urban Development Authority if the local politicians can't put their Nimbyism aside.
Key's own inaction has created another political vacuum which Labour leader Andrew Little will try to fill with a string of policy announcements over the weekend.
Put the politicking aside, though. The general election is not until late 2017. The time for a balanced compromise for Auckland is now, not then.
The brutal truth is that Key and Wheeler need to realise that their elegant pissing contest is not solving the issue.
