Thanks everyone for commenting! You gave good arguments for not having any channels in the standard library and, honestly, I’d be happy with that outcome.
I want to remind that the mpsc implementation has been broken for years and needs to be fixed one way or another as soon as possible. So we need to do something about it.
A serious bug that is trivial to trigger was reported two years ago but the complicated codebase makes it difficult to fix. There was a PR attempting to fix it, got blocked on removing mpsc_select (will be a big refactor), and was subsequently closed. The bug is now even documented as a known issue, which is a bad look for Rust and doesn’t inspire confidence in the quality of our code. 
And even if we fix the bug, I still think the API has so many flaws it would be better to not have it at all.