I've noticed this happens across cultures as well, notably the German "Zack-zack" and the Indian "Fatafat"
These phrases seem to have a repeating motif of some sort; reduplication with "Zack-zack" and "Chop-chop", alliteration with "Ship-shape" and "Zip-zap", and what I can only describe as "internal consonance" with "Lickety-spilt" and "Fatafat"
They all amount to "Quickly", but I can't quite identify what aspects of theirs make them seem so naturally adapted for the expression, and I want to understand it, if only because the information would be quite useful to help create similar half-nonsensical phrases