The previous trend, lasting about twenty years, was for J names - think
Jason, think
Jennifer. So maybe the trendoids have just moved one step down the alphabet!
There's often a feeling that if you change the spelling of something, it becomes less of a word and more of a name - though in fact the capital letter and the context do that perfectly. So, since K is an unusual letter for English words to start with, it might look pleasantly distinctive for a name to start with. Who knows how people think when confronted with a nameless baby?
Two of your examples,
Carter and
Kennedy, are part of the surname as first name trend - an odd one in my view; presidential choices, OK if you're fond of presidents, but not to my taste.
So you've actually found two separate trends working together! Interesting ... and thanks for sharing.