We've used this technique for as long as I can remember. We called it a scissors. Rarely saw an injury to either the thrower or the "scissoree" - either in competition or training.
Back in the seventies and eighties I used it in Karate tournaments in New England quite often. Earned a point the times I scored with a follow up. The only injury I got was from a gentleman, Billy Polk, who I believe was a Shotokan practitioner. He reversed punched me to the side in the middle of my take down. Broke two of my ribs. They gave me the point, which they shouldn't have because his punch was first. Billy was a great guy and could punch quicker than I imagined.
In the eighties, Billy Blanks taught me a head scissor take down. Same motion with a jump - top leg going across the front of the throat and trail leg going across the lower back (angling down from the shoulders) Blanks used to score with it all the time. (he had some serious hop) I pulled it off several times in competition as well. I missed it once - the guy ducked and went left - I crashed to the floor and caught a stomp to the chest. (good, legal point back then)
We used to teach scissors with a spotter. Student in a side stance, spotter right behind him in same stance. Spotter would put his arms around the student's back/chest (unclenched) and get the student used to thrusting his lower body ahead of his upper body. The spotter allowed the student to get the feel of the lower body thrusting forward without having to crash to the mat too many times. The biggest mistake students usually make is not extending that bottom leg. They tend to have the knee bent and jam themselves. Using a spotter allows the student to concentrate on that bottom leg really reaching.
Sometimes, during big classes, we would do a "scissors line". We'd lay out the mats in a long line with fifteen people all in side stances about 8-10 feet apart. You would scissor the first guy (who would purposely go down) then scramble up and go to the next guy. it seemed to work well, once you were fairly adept at the scissors - doing it fast going down a line really helped with your speed and taught you not to hesitate.
We also used to do a spinning scissors. (a 360 as opposed to like a turning back kick) probably not practical, but it was something to do to help body control. The spinning scissors took a person down fast and hard. Speaking of which - when we did a regular scissors in dojo sparring - the scissoree would reach out and cup the back of the head of the guy you were taking down to insure he didn't crack his head. Seemed to work well.
I never even considered it for BJJ. I competed in a few BJJ tourneys, but there were far too many ways i got smoked - didn't need a scissor take down to help me get whooped.
