Griffiths is a gifted footballer, whose knack for dramatic, exciting goals is not in dispute, but whose other characteristics have left a lot to be desired.
Bringing morality into these debates is always a dodgy exercise, though it can hardly be outlawed. Fans of Celtic or any other club have a perfect right to voice their views on it.
One reason why many Sunderland fans objected to Paulo Di Canio's doomed arrival last season was because, on moral grounds, some detested his political views. It's as well they weren't told to clamp it and leave their pesky principles elsewhere.
In the case of Griffiths, there is much not to like, frankly. The striker has a history of unsavoury behaviour - of gestures, of at least one racist outburst, not to mention a chaotic, contemptibly selfish private life - which people find off-putting.
Then there is the story of Mick McCarthy, the Wolves manager who paid £150,000 to sign Griffiths from Dundee in January 2011, but who immediately found him to be an unpleasant character, and had little time for him.
Griffiths has frequently been referred to as "a ned", which is often a rash and unfair tag, though much of his activity has brought that upon himself. It seems beyond dispute that, in some areas, he could raise his level of human decency.
The counter-argument is this. Griffiths is still just 23 years old. He is a product, to some extent, of his background. He has plenty of growing up to do and, many attest, has sufficient character about him to do just that.
Last season, in at least one interview he gave following a Hibs match, Griffiths surprised many by talking openly and well, and in a way that belied the reputation that went before him.
Moreover, I can think of some footballers I know and admire today who, when I first met them in their early 20s, seemed little short of yobs. It is quite a testimony to football that it often makes better people of its workforce.
On the park, in my view, there is little to dispute about Griffiths' ability. His skill and goalscoring have been there for all to see over the past five years.
Last season, during which he scored 28 goals in 42 outings for Hibs, Griffiths' game was often thrilling. He scores all types of goals, not least the intermittent screamer. He also has that godsend for a centre-forward: he simply cannot stop believing in himself.
Peculiarly, despite being Wolves' leading scorer at the turn of the year, Griffiths' manager, Kenny Jackett, has omitted him from five of his last seven starting XIs. This has only proved to be a further, complicating factor in the Griffiths debate.
Jackett has targeted a number of new strikers, including Coventry City's Leon Clarke. His view of Griffiths appears to be that he is difficult to play in harness with someone, that his instincts are too erratic, too singular for the team collective.
It is an odd view, given the 13 goals that Griffiths had scored by Christmas, and the public hankering by many Wolves fans for Jackett to start playing the striker from the start. But none of this need be Celtic's concern.
On the basis of last season, there were grounds for Celtic trying to sign Griffiths last summer, but they chose not to. Now, however, Neil Lennon sees a new window of opportunity in getting the player.
Never mind the other aspects: could Griffiths make the step up from the English third tier to play for Celtic, domestically and in Europe? Yes, absolutely.
Gary Hooper went from Scunthorpe United to being a success at Celtic. Scott McDonald did likewise, having been a Southampton reject before finding himself again at Motherwell, and then at Parkhead.
Andrew Robertson is a current case of a player making quite a leap from Queen's Park to Dundee United, and is utterly thriving.
Football is littered with such examples. In many cases, talent and ability will out, no matter the level required. And in some scenarios - as the "reject" Henrik Larsson showed back in 1997 - the outcome can be astonishing.
Off the park, I've been no admirer of Leigh Griffiths up to now. On it, I've never doubted his fine ability.
My hunch is that, if he came to Celtic, and started scoring goals, this debate would swiftly cease.