Hmm, apparently 'behavioural modernity', 'most recent common ancestor' and 'out of Africa' are all around 50 000 years ago.
Until about 10 000 years ago a great deal of the world was under thick ice sheets, and probably a lot of the rest was cold, so there probably weren't that many humans alive.
If you give each living person a tiny chance of 'inventing agriculture', then "multiple recent inventions thousands of years apart" sounds about right to me.
I realize that that's a completely implausible model, but I'm not sure why a more realistic one would make it 'too ridiculous to be a coincidence', and if you require plant evolution as part of the scheme, that will push the expected dates later.
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Your argument depends on choosing what's "central" or "archetypal" example, and that's completely arbitrary, since this doesn't seem to mean "most common" or anything else objective.
It really falls apart on that.