The view is that when Williamson leads, he has a fresh sheet to work with rather than any lingering glances at the man prowling around mid-off, either for guidance or approval.
But Williamson is expected to captain New Zealand in their five T20 internationals against the two sub-continental teams next month. McCullum's days in the shortest form are over.
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He's not going to the World T20, meaning it's time to look ahead, however, Hesson was emphatic on one point.
"Brendon is still our best captain. We've obvious got a number of highly-competitive games so, if we had the option of having Brendon available, we'll certainly use him."
Hesson insisted McCullum remains highly motivated.
"He's fully committed to the team until the end of the test series against Australia and obviously wanting to do well."
McCullum said he'd rather have waited until the end of the second Australian test in Christchurch, starting February 20, to make his announcement. The need to name the World T20 squad, likely to be on February 11, worked against that and there was also a desire to avoid rumours and speculation distracting the side.
McCullum, though, wasn't about to start ruminating on his career just yet. That will wait until after Christchurch.
"I've loved my opportunity to play for and captain the Black Caps, but all good things have to come to an end, and I'm just grateful for the wonderful experience of playing for my country," McCullum said.
His body has been "a bit sore for a while" but McCullum insisted giving testimony in the Chris Cairns perjury trial in London had no impact on his decision.
• McCullum on Cairns trial: I stand by my evidence
Certainly while last year was a stellar period for the 34-year-old - the first test triple century by a New Zealander, the most runs in a calendar year by a New Zealand player until overtaken by Williamson in Hamilton on Monday - there had been no hundreds this year.
Making the World Cup final was the standout leadership achievement.
There was the stress of the Cairns trial, nothing remotely akin to the pressures of sports captaincy, and the inescapable impression that he was worn out.
His second-innings dismissal against Sri Lanka in Hamilton on Sunday - when he charged down the pitch and heaved at a delivery when victory was both within sight but also still tantalisingly some distance away - seemed a pointer to that.
However, McCullum admits he had not mentally checked out or let future thoughts affect him this year.
"I'm an either all in or all out kind of bloke," he said.
Instead, he thought he probably hadn't been in top form with the bat and had played some "terrible" shots, which he joked had probably "plagued my career".
The world's T20 circuit is in his sights. McCullum has a three-year deal to play for the Brisbane Heat in the Big Bash League and a contract for the new Indian Premier League franchise based in Rajkot for a cool US$1.6 million. His attention will also turn increasingly to his horse racing and family interests.
So how will New Zealand' 28th test captain be remembered? Certainly he has been the country's most daring captain.
Perhaps more than anything, he allowed the country's fans, especially the younger ones, to dream what might be possible.
He has risked defeat in search of victory, and that policy inevitably guarantees not all days are golden.
But he will be remembered far more for the ups than downs and as a leader who helped New Zealanders embrace the game, and rejoice in what their team achieved and the spirit with which they played it.
