"Kids" v. "Children"

From the late, great man-of-letters Kingsley Amis, who had a better built-in bullshit detector than most:

Kids
This word for children, labelled an Americanism by COD, was until about 1970 entirely colloquial and conversational, with no special overtones. Then it started to become a teachers' and educators' term for schoolchildren, feature in the boast, 'We [in our dedicated way] don't teach subjects, we teach kids.' It now turns up in serious places like the letters page in The Times, if that is a serious place. Kids in this sense will fade soon, though not soon enough to suit me.

My objection to its 'committed' use is not to be traced, I hope, to my being snooty, old-fashioned, old or British. No, this use carries a strong hint of being down-to-earth on purpose (see Belly). It condescends to children and robs them of their dignity in just the same way as it denatures an Italian, say, to call him a wop.

To me, dubbing children kids out of policy recalls the affected chummy docking of Christian names for public use at the head of articles and such and even at the foot of letters to The Times. Let me be the one to decide when if eve to address you or refer to you as Chris, Ken, Dave or Jim.

-- from The King's English (1997).