Hi Bill,
I think you have misunderstood the biology here. Prior to the evidence of continental drift, ornithologists were indeed puzzled by the appearance of paleognaths on multiple continents:
Most recent studies have also strongly supported ratite monophyly (9–12, 14), suggesting a single loss of flight in their common ancestor. This puzzled biogeographers for more than a century, because ratites would be unable to achieve their current distribution on southern land masses if their common ancestor was flightless.
However, the puzzlement ended when continental drift became understood:
Continental drift provided a compelling solution. No longer was it necessary to imagine giant flightless birds crossing vast oceans; they could have rafted to their current distributions on fragments of the Earth’s crust (15). Although the proposed phyletic branching patterns for ratites do not correspond perfectly to the order of separation of land masses during the breakup of Gondwana, the convenient serendipity of continental drift as a mechanistic explanation for ratite distribution proved irresistible (10, 11, 14, 16), and it stands today as a textbook example of vicariance biogeography (17, 18).
So ornithologists weren’t scratching their heads, flapping their arms, muttering “We just can’t figure this out, how did those emus and ostriches and rheas scatter to the four winds? Oh, it must have been convergent evolution!” No, they had a highly plausible solution (continental drift) that did not require convergent evolution.
Very recently, the paper you cited announced that, based on analysis of 20 genes, there are three phyla among the paleognaths. It was only the DNA evidence that suggested that convergent evolution explained the distribution of flightlessness among paleognaths.
Convergent evolution is a concept that has been around for almost a century and a half. I do not see anything unscientific about the idea that similar natural selection pressures would favor similar adaptations. It almost seems trivial.
My $.02.
Warm Advent wishes,
Chris Falter