This claim is situated in the context of a fight in psychology between the traditionalists (who want published work to stand untouched and respected for as long as possible) and replicators (who typically don’t trust a claim until it is reproduced by an outside lab).
Rather than get into this debate right here, I’d like to step back and consider the proposal of Kaufman and Glǎveanu on its own merits.
I’m 100% with them on reducing barriers to creativity, and I think that journals in psychology and elsewhere should start by not requiring “p less than 0.05” to publish things.
Nothing is stopping researchers such as the authors of the above paper from publishing their work without replication. So I’m not quite sure what they’re complaining about. They don’t like that various third parties are demanding they replicate their work, but why can’t they ignore these demands.
Indeed, as I wrote above, I think the barriers to publication should be lowered, not raised. And if an Association for Psychological Science journal doesn’t want to publish your article (perhaps because you don’t have personal connections with the editors; see P.S. below), then you can publish it in some other journal.
If, you flip a coin 6 times and get four heads, and you’d like to count that as evidence for precognition or telekinesis, and publish that somewhere, then go for it.