Those two statues, just off King's Avenue in Barton, capture John Curtin and Ben Chifley, the 14th and 16th prime ministers of Australia. Taken from a photograph, their pose seems eerily true to life. Both men are formally dressed, wearing hats with three-piece suits, but that is the outer limit of formality. The two are off to work, wandering placidly down the street, chatting to each other between the Hotel Kurrajong (where they lived) and Old Parliament House (where they dragged Australia through World War II). In a reversal of government hierarchy, the prime minister is insistently making a point, while his treasurer listens as he quietly puffs on his pipe. Theirs is mateship in its platonic form.

In the compass of Australian public architecture, as in the annals of Australia's governance, there is nothing like those statues anywhere else. The amity between Curtin and Chifley might appear unlikely: lonely, stranded, recovering alcoholic meets dour train driver to play bridge. Nonetheless, that friendship – then the trust and mutual dependence that underpinned it – sustained Australia through many of our worst days. Why, then, are there no comparable partnerships in the political history of Australia, and possibly other democracies as well?

The obvious answer is that government makes room for only one president, one prime minister or one pope at a time. Although those leaders usually operate through cabinets, work with ministers, and are accountable to both parliament and electorate, they are still the boss. During a world crisis for democracies, Winston Churchill reserved as much power to himself alone as possible, while Franklin D. Roosevelt deigned to meet his last vice-president only twice in private. That, of course, was the same period Curtin and Chifley were chatting away.

More collegial models of leadership exist but in other domains, places like the High Court, the Reserve Bank or an operating table. In another permutation of power, trios, rather than couples, have been tried with mixed results. Think of the sorry fate of every Roman triumvirate and the unlikely fictional tale of The Three Musketeers. As for quartets, that arrangement only works with strings and The Beatles.

By contrast, for political leaders, distance – cultivated, haughty distance – lends enchantment to the view. That said, leaders must still affect false modesty. Crises, the media and Australian rowdiness impose natural limits on aloofness. No Australian political leader could afford to emulate General Charles de Gaulle's insistence that any good decision was necessarily grounded in silence and solitude.

In addition to haughtiness, those whom we elect to high office may seek to surround themselves with a firebreak of mediocrity. Putative rivals might be pensioned off or sinecures found for them. Hence another splendid statue, on the other side of the lake, shows Bob Menzies striding quite alone. Thinking he had no peers, he discovered he had no mates. To hark back to the Bible for markers on partnerships, neither did Cain and Abel, nor David and Jonathan.

Aloofness possesses psychological as well as political dimensions. That may explain why president Harry Truman advised a colleague that, if he wanted a friend in Washington, he should acquire a dog. The Kennedy brothers, Jack and Bobby, enabled and empowered each other but may have led each other astray, too. As for the more recent pairing of Bob Hawke and Paul Keating, in retrospect that resembles Jack Sprat and his wife, with neither possessing nor esteeming the other's strengths.

Behind and beneath tactics of political survival might lie a few essential character traits. One brand of leader just does not excel at sharing her or his toys, distributing praise or permitting others' reputations to shine too brightly. Such leaders may deprecate political partnerships because they are convinced no one could replace or supplant them. Term limits are a good remedy for folk like that.

Repeated evidence of human frailty does not persuade leaders of their own mortality. Just consider the paltry number of Australian politicians who have left on a high, on their own terms and at their own time. The last Australian prime minister who left precisely when and how he intended to was Frank Forde, who held office for one week only.

Too many political partnerships leave the junior partner playing a role uncomfortably like those of traffic cop, cheerleader or psychiatric nurse. Politicians doing jobs like those can turn into latter-day James Boswells, Sancho Panzas or Dr Watsons. After all, Chifley, not Forde, was the prime minister's confidant on his morning stroll. Treasurers may console themselves that they are doing the tough, grunt work and thereby earning a chance at succession. Chifley did, as did Harold Holt and Keating later. Vice-presidents might muse about their bosses dying in office. Enough (eight so far) do to give them heart.

The most audacious recent twist in political partnerships is surely Bill Clinton's decision to co-write a political thriller with James Paterson (The President Is Missing, published by Alfred A. Knopf and Little, Brown & Co, June 2018). That story, about an intrepid war-hero president who foils a cyber attack on the United States and humiliates Russia as a side-benefit, is pure wish fulfilment. Churchill reckoned he would do well by history because he was writing the historical record himself. Even so, Churchill could embellish and embroider only up to a point. Clinton, by contrast, has entirely reinvented himself. His fictional president is unsullied by lust, untempted by political calculation, untroubled by bullets, unfussed by illness or treachery. We should update Harry Truman's advice. If no dog is available, get a co-writer.

Mark Thomas is a Canberra-based writer.