Invented by dance teachers who take pity on their students and do not care to force ballroom terminology down their throats more like.
Actually I hear ballroom teachers using the "quick, quick, slow" terminology as well. I don't think its because
they don't know better. I think its because when you are trying to teach a middle aged, non physical agile person who has NO dance training and NO music training how to dance a structured partnered social dance as an adult, the student has all they can deal with just to figure out basic steps in the beginning and not step on their partner.
Trying to explain Fox Trot, or worse, Cha Cha using musical counts to instill the correct rhythm adds more than the student can process sometimes, so they just tell them to think "Slow, Slow, Quick-Quick" (for fox trot) or rock,step,chachacha (for Cha Cha) The students usually hear what they need to hear in the music, they just don't understand the music theory that is behind it.
The fact that the count for the chachacha part of cha cha
isn't the 3&4 counts is more than they can take in in the first couple of lessons and definitely more than they want to know. You can see the flashing
TOO MUCH INFORMATION sign go off in their eyes. If nothing else, beginners have a great deal of trouble starting on the correct '1' in cha cha. Its FAR easier to start on the 2. They hear the 4&1 as a 'set' and starting
during it is hard.
So I have no problem with the idea of using whatever gets the rhythm into the people's heads and saving the complex music theory for a lesson a little further down the road. People go to their local dance studio to have fun and learn to dance (sometimes reluctantly at the urging of their spouse) If "Quick,quick slow" gets them moving correctly and ENJOYING it, and correct music theory makes their head explode, then 'quick, quick, slow' it is!