I might have missed it, but was the song regarded as negatively and cynically in 1996? I genuinely don't remember it being so. I just remember thinking it was a pretty catchy and better than normal football song, but, now I look at the phrase "it's coming home" and agree that there is a degree of arrogance involved in it.
That seems odd to me - why didn't I feel like that twenty five years ago? I think you're right to a large extent in saying that the song was written with a degree of good humour and affection, but I'd also say that the sort of response I have to the term now is down, to a large extent, to how polarised the world has become - I don't like this trait in myself, but I'm less likely these days to see the humour in things and less inclined to give others the benefit of the doubt compared to a quarter of a century ago and I think I'm far from alone in being like that, the world is a less friendly place than it was.