I was expecting an explanation about the initial request.
Is there an oversight (??) or an another reason to not have a
Barrier primitive in asyncio ?
Probably because nobody working on asyncio at the time had any experience using threading.Barrier. I know that I have used all the other primitives, but I don't recall ever having used Barrier. I don't think there's anything deeper than that. You should probably just open a bpo issue (mention this thread) and submit a PR linked there. I can't promise to review it though. :-)