I find it rather peculiar, though, that the crossbreeding of species, or bestiality, angle of the dream/desire is always ignored completely.

Gotta have those feathers.
That seems a stretch, pardon the pun.
In science fiction involving space travel, the implication is always that a bird lineage evolved into higher intelligence, i.e., human. It's quite likely that anything more like birds in body quickly was discarded due to costumes inevitably having a comic Chicken Man effect that doesn't serve sci fi fans' fantasies.
Multiple animals have evolved to fly: bats, birds, bugs, and even some snakes and lizards, although gliding, not self-powered.
Man merely dreams of flying, just as he does of diving and seeing the underwater world, also a dream until mechanical means made it possible.
The fantasy is likely expressed in terms of feathers because bats have had a negative image in the West, unlike in China and some other places. And bugs are seen as vermin in most of the world, or at least the areas where we aren't eating them.
But, even though I disagree that anyone imagined bestiality as the precursor to "birdmen," the morphing is a good point to analyze. My guess is that men envy birds not just for their flight, but for the power it gives them, even freedom. War birds are a common icon in many cultures, so raptors and their strength surely is a part of the birdman envy.