"I see no particular advantage in preserving urban legends."

Urban legends are very vibrant aspect of current folklore. And they reflect real patterns of fears and of social preoccupations.

Surely the point here isn't that the link between the song and the plague is recent, but that the evidence so far isn't there. And it seems highly unlikely that the kind of evidence that would be required is going to turn up, because it's the kind if stuff that gets recorded. It could of course - some diary or letter in which someone talked about listening to some children playing, or a sermon about the fragility of life in face of the plague, quoting the rhyme... But nothing has turned up so far.

Until and unless it does, it's pure speculation, based on a sense of what sounds right poetically, which doesn't mean it might not be true, but certainly doesn't mean it is true either.

However, as has been mentioned, this suggestion has become current to such an extent that it colours how we hear the rhyme nowadays. I suppose that's what calling it an urban legend means. And as an urban legend, or something analogous to that, it has its own enduring strength, irrespective of whether it actually coincides with historical truth.

It rings a bell with us, because we are aware of the sense in which children playing are playing in the imagined presence of death and devastation. And that is an echo of the century we have gone through, with its wars and genocide, and the nuclear threat hanging over us - and it continues, changing, but never letting up. So the song has somehow come to relate to our own Plague time.