~"Kate vanished as quickly as she appeared, not to be spoken of again until recently, whereas Batgirl continued to appear in a bunch of other publications (though admittedly none of them very good), joined the Outsiders and eventually even got her own series' back (though again, not a very good one)."
You're looking at this retroactively. Majority of that happened over a year after OYL. The few appearances she did make, Cass was a villain.
Like the other poster said, this was done in reaction to OYL. During OYL Cass became a villain. She wasn't the Bat female anymore. As for Batwoman, there continued to be talks of her series starting for several months. Nothing came of it. But as far as OYL goes, Cass was pretty much kicked out of the Batfamily while talks of the Batwoman series continued so the cartoon reflects that time from over two years ago. They didn't know what DC was going to end up doing with either Batwoman or Cass.
Perhaps I'm used to Casstoons, but I figured this was mostly a parody. Don't parodies over-exaggerate things?