For some, these things will loom large in the assessment of his term. But the critics need to look past an economy that has seen some of the best GDP and employment growth in the Western world since 2012. They'll have to ignore the fact Wheeler ends his term with inflation back in the official target band - despite historic deflationary pressures, both structural and cyclical, still stalking the world.
He departs with the official cash rate so safely set in neutral that debate about whether it should go up or down is not focused on October or December, but on 2018, 2019 or even 2020.
Should the global economy collapse, Wheeler's successor, with the rate at 1.75 per cent, will have seven cuts up his or her sleeve. The US rate is still just 1.25 per cent, the UK 0.25 per cent. Europe is still at zero and Japan is negative - where they go in another crisis is anyone's guess.
Then there is the housing market, remarkably reined in after the introduction of a series of bold and often unpopular macro-prudential lending rules. It is perhaps the Reserve Bank's greatest success under Wheeler.
There may have been fair winds with other factors slowing the market. But loan to value ratio (LVRs) were constructed and implemented with a view to a shift in market dynamics that appears to have played out perfectly. Although we're far from out of the woods on private debt and asset bubble risk, our economy is in a much safer place than it might have been.
He has had some luck. The Reserve Bank was caught by the commodity collapse in 2014 and had to unwind a series of rate hikes. But the New Zealand economy was robust enough to withstand the shock and did not go into recession.
Wheeler has not been afraid of upsetting people if he thinks a point needs to be made. That in itself seems to have upset some people.
There have been suggestions he clashed with the Government.
One suspects relations were never chummy with former PM John Key. But that was never as important as the relationship with the finance minister.
Wheeler has been happy to publicly stress the quality of his relationship with Bill English and Steven Joyce. It is a view backed by English and Joyce.
That's beltway stuff, anyway - a running soap opera for economists and monetary policy obsessives.
Stepping back, Wheeler has fulfilled another crucial requirement.
He has been a champion of deep and detailed thinking, unashamedly putting intellectual considerations ahead of his media profile or popularity.
When you think about the pressure on public figures to be relatable - politicians dabbing and twerking, planking and Instagramming their pizza - our central bankers are a last bastion of undiluted intelligence. Wheeler has been a torch bearer in that role.
I've met him for numerous off-the record briefings with groups of journalists and for one-on-one interviews. They have always been fascinating discussions.
When you ask him a question, he doesn't come back fast with a snappy reply. He pauses and lets the silence hang there as he considers all the angles on the question and constructs a response.
Those answers are often illustrative, drawing on historical examples. His recall of statistics and distant economic events is staggering.
Yet after hours of discussion I don't know what his favourite movie is, or his favourite band. I've never asked.
Based on his intellect, his education, career and travels I'd imagine he has good taste. He may even have been cool once.
He backpacked the world in the 1970s, sleeping rough and living on his wits. But you won't catch him tweeting about Taylor Swift to add a quirky human touch to his social media brand.
And that's a relief.
The professional distance that has been built into the code of central banking is there because even the most subtle comment can move markets.
But it has a broader virtue in an age of personality politics and celebrity news.
Like test cricket, poetry or jazz, central banking has a form and a structure. It is to be celebrated and protected. It is something Wheeler has honoured.
