"Perhaps they love and clasp this usage as a rule
Because a favourite teacher taught 'em it at school."
(School of #PopeNotPontifex)
I made the mistake of bringing up the "which vs that" controversy on Twitter recently. I was immediately involved in a discussion with, I think, well, I'm sure, an American correspondent who really does love that "that for restrictives / definitions - which for extra information" pseudo-rule, as @StanCarey calls it.
In that last, rather long sentence I used a restrictive (UK used to say "defining") relative clause. Why don't US writers, or more importantly editors, have similar problems with other wh- words? What about:
"The house where I was born has been demolished.
The house, where I was born, has been demolished."
The same problem (?) may / must exist, if less often, with "when". I suggested that it was mainly a problem of punctuation and that people just need to read aloud (or with internal voice) and decide whether they pause (add comma) or not.
It is true that it may be useful for harried and hurried journalists and subeditors, or people unsure of commas, but it is a matter of usage and punctuation, not grammar. Those who have been taught this usage as a "rule" - it is certainly not a rule in BrE, see standard grammar books and e.g. British Council Learn English website - seem to be fond of it and sometimes get self-righteously cross about it.