Isn't your experience highlighting what the article is suggesting though? That needing to do this during an interview is what causes these failures rather than an inability to actually perform the requested task.
It seems like the suggestion is to put them somewhere private to perform the task rather than asking them to do it in a public setting.
The rub is the take home assignments are not good either.
I do personally let people pass the tech if they have good open source work (a good tech blog, legit python repo's, not just trivial homework stuff they did in school). So few of people have that though.
But the thing in the study cited in the post was putting people alone in a room for the same task with the same time limit -- _not_ take home assignments.
What if this is just a (labor-saving) tweak to on-site live coding interviews. You've already reserved the room. The status quo is that a member of technical staff is in the room with the candidate for the duration of their interview. The low-cost alteration is, after you explain the task and make sure it's clear, you leave them alone in there for the remainder of the period. Perhaps the interviewer gets a few small work tasks done while waiting outside.
I think the only unfortunate thing is that when you're in the room trying to talk to them about their solution as they write it, sometimes you can have a helpful discussion, which may involve probing or leading questions, which sometimes give you some signal -- but these also make it much more difficult to compare across candidates, so perhaps we should be ok letting go of that opportunity.