That hasn't stopped plenty from doing so. Those who know their history really shouldn't be surprised that the club has been attracted to a candidate who splits opinion. They nearly always are. In the last 15 years Jo Venglos, John Barnes, Gordon Strachan, Tony Mowbray and Neil Lennon have all been the permanent manager of Celtic and every one of them arrived accompanied by a considerable element of risk.
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Each stood there on day one with the obligatory green-and-white scarf raised above his head for the photographers, and an invisible question mark hanging higher still. With Venglos it was his age and ignorance of the Scottish scene, with Barnes and Lennon it was their total absence of managerial experience, with Strachan it was a mixed previous record, with Mowbray the unfamiliarity with the pressures felt in a job as big as Celtic's.
One name is missing from that sequence of managers. Only Martin O'Neill arrived at Parkhead free from any meaningful doubts. The days of Celtic being able to pluck a rising managerial star out of English football, as O'Neill was in 2000, are long gone. So should supporters now unquestioningly accept any name presented to them, such as Keane? No, but a recognition of the market they are in and the priorities of the major shareholder Dermot Desmond, make Keane an unsurprising focus in the search.
Searching "Roy Keane" on Twitter over the past 48 hours has produced endless mentions, the vast majority negative. Social media is a useful window into how supporters think about club activities, but only up to a point. There can be a disconnect between more vocal keyboard fans and those who go to games (and when they are one and the same, a disconnect between how the same person behaves online and in a ground). There was similar online hostility to Leigh Griffiths's arrival at Celtic in January but when he made his debut, as a substitute against Aberdeen in the Scottish Cup, he was loudly cheered.
It's easy to think of Keane as a "bad" manager. It's seductive, even amusing, to do so. The idea of the uber-winner, the warrior with the insatiable appetite for victory, being some sort of hapless figure in a technical area is compelling because of the stark contrast it offers between player and manager. The great player as bungling manager is one of the oldest stories in football. But if Keane does take charge at Celtic in the coming days it will show that the club is willing to take a punt on one of the British game's intriguing imponderables: namely, might Roy Keane still make it as a top-class manager?
It was not as a psychotic training ground enforcer that O'Neill picked Keane as his assistant manager for the Republic of Ireland in November. O'Neill can handle discipline perfectly well on his own, without having to find someone to do the sergeant-major act. He brought him for his experience, intelligence and coaching. That's a powerful endorsement. And from day one O'Neill let it be known he knew their partnership was on borrowed time because he was certain Keane would again be offered a job as a manager.
Writing off Keane at 42 is absurd, and so is exaggerating the extent of his "failures" at Sunderland and Ipswich. Most of the damage done to his reputation was inflicted (self-inflicted) at Portman Road. They started horribly in 2009-10 and finished 15th. The following season began with one defeat in their first eight and a run which took them to the semi-finals of the Carling Cup. But the league form collapsed and Keane's number was up.
He was sacked there. He was not dismissed by Sunderland, his first club. When Keane arrived in August, 2006, Sunderland had lost four on the spin and were second bottom of the Championship. Under him they won the league and promotion to the Barclays Premier League. He was awarded the division's manager of the year award. The following season he kept them up, and did so pretty comfortably with survival guaranteed with two games to spare. They began the following season poorly and it was his decision to leave before the halfway stage of a campaign in which there was still time to arrest their declining form.
What it all amounts to is a patchy record, not one to write off. Three-and-a-half years have passed since the bruising Ipswich episode. That's a lot of thinking time for a man to contemplate what went wrong, how much of it was his fault, and how best he might adapt to make a better job of things next time. Keane is a compelling presence as a pundit and while those are not transferrable skills when it comes to re-entering management his studio appearances also act as confirmation that he remains demanding and perceptive.
There was tension with some players at Sunderland and Ipswich. He was intense, uncompromising. and management no longer accommodates one-dimensional drill sergeants. Keane must know when to cuddle as well as when to kick a backside, or else the chance he might get at Celtic will be his last. The move for him is no mystery. He will draw interest, attention and supporters to Parkhead. And Keane got men to play for him as an inspirational leader on the field. Celtic aren't alone in reckoning he might yet amount to something on the side of a pitch too.