It was an unusual suggestion from an unexpected source and it signalled the extraordinary desperation that pervades the thinking of some of the region’s most senior leaders.

It occurred earlier this month when Singapore’s Prime Minister Lee Hsien Loong, while on a visit to Myanmar, asked State Counsellor Daw Aung San Suu Kyi to use her high global profile to burnish the tattered image of ASEAN.

Right now, the discredited Association of Southeast Asian Nations is drowning in bitter and treacherous waters, where the sense of betrayal and the desire for revenge run high. It is not a pretty picture.

As the former Thai foreign minister and ASEAN secretary general Surin Pitsuwan lamented, there are presently no “towering leadership voices” with the gravitas to bring harmony to the group’s bickering members.

In the past, Indonesia’s President Suharto, Malaysia’s Mahathir Mohamad and the Singapore PM’s father, Lee Kuan Yew, would never have allowed the situation to become so rancorous.

It is now so bad that sober analysts openly discuss the likelihood of a regional equivalent of Brexit, with nations like Singapore wondering whether to cut their losses and exit the group.

ASEAN’s current malaise was heightened by the comedic catastrophe that occurred two weeks ago at a meeting of the group’s foreign ministers with their Chinese counterpart in Kunming.

It was an echo of an earlier debacle in the Cambodian capital of Phnom Penh in 2012, when, bowing to Chinese pressure, the group’s furiously squabbling members proved unable to issue a joint communiqué.

In Kunming, things turned even worse when an attempt to express serious concern about developments in the South China Sea was thwarted by Cambodia and Laos, who again capitulated to Chinese arm-twisting.

Remember, under ASEAN’s outdated but sacred “rule by consensus”, no statement, policy or strategy can move forward unless approved by all members.

Unfortunately, although once they could agree, especially when guided by the likes of Suharto, Mahathir and Lee, today they cannot.

The group is currently governed by the politics of grievance and it is a friendly association in name only – and it may not even be that for much longer.

Already, in the aftermath of Britain’s Brexit vote to leave the European Union, there is talk that something similar may happen here.

As Donald Emmerson, a regional expert at California’s Stanford Institute for International Studies, said this week, “Will Brexit prompt Singapore to leave ASEAN? A Sexit?”

It is not impossible. The Singaporeans are angry at what happened in Kunming and are pondering the point of remaining in a group that diverges more than it converges, and does so in a very acrimonious way.

A similar sentiment may well prove infectious if the Kunming debacle is repeated at the group’s ministerial summit in the Lao capital of Vientiane next month.

After all, why should a powerful nation like Indonesia, for example, continue to put up with stubborn pro-Beijing recalcitrance from Cambodia and Laos?

Certainly, the association’s achievements over the past half century have been meagre. There is still no single visa, no common currency or regional parliament, and the ASEAN Economic Community, launched earlier this year, has brought little, if any, increase in intra-group trade.

Consequently, few doubt that if a referendum were held in prosperous Singapore or Brunei, or even in thriving Indonesia or the Philippines, a majority would vote to leave the feuding group.

That such thoughts, however improbable, are even in the air is a mark of how bad the situation has become, and they help explain the Singapore PM’s extraordinary approach to Daw Aung San Suu Kyi.

Regrettably, his proposal for her to act as the voice of ASEAN on the world’s stage is misguided in the extreme.

After all, she has only been in government a few months and has little experience of hardball exchanges with other leaders, especially regarding matters of national sovereignty.

Yes, after her quarter-century pro-democracy struggle, she has a sky-high profile across the world – although, perhaps not unexpectedly, it is less high within ASEAN than it is outside.

But within the corridors of power, her glowing reputation will only go so far, and it will not even go that far against superpowers like China, Russia and the United States if she espouses a view contrary to theirs.

If, for example, she were to endorse a statement expressing concern about China’s behaviour in the South China Sea, she too will engender the opprobrium of Beijing and find herself at odds with Cambodia and Laos; whereas if she does not openly support her fellow ASEAN claimants, then they too will soon turn sour on her – and so will Washington, which tacitly backs them.

So it is a lose-lose situation for her and she should not be burdened with trying to sugar-coat the profile of ASEAN in international forums like the G20 and the United Nations, if the grouping itself remains divided.

After all, who is she supposed to be speaking up for when she “represents” ASEAN? Outliers like Cambodia and Laos? Military-ruled Thailand? Sharia-inclined Brunei and Malaysia? Communist Vietnam?

No, Daw Aung San Suu Kyi is not the one for this job. Not only does she have so much else on her plate, but also she was never cut out to polish ASEAN’s tarnished image nor to stop the growing Sexit sentiment.

The offer from the Singapore PM was a poisoned chalice that she should firmly reject.