Do you want to practice falling or not practice falling? There's your answer. Kicking the feet before the hands hit is practicing falling.

Hey Bengi, this post may help, specifically the check out the caption: https://www.instagram.com/p/Bx9wtFJgwqS/

I noticed the same thing, Bengi. I have been coaching and CrossFitting for 10yrs and am unfamiliar with a burpee requiring a rigid body (as in a push-up), and this includes the Open. My guess is that one can improvise the ground portion based on their fitness. I do see folks who are very fit utilize a push-up and seem to have extraordinary efficiency with it, but I, personally, can’t. I have always performed and coached the burpee as 1) get chest and thighs on the ground 2) get back up to your feet 3) get some daylight under your feet. Furthermore, I prefer touching my fingers to a target in the burpee to ensure a reach to the sky during the jump. 
 Either way, variety is the name of the game, and there’s room for lots of burpee variations. Sometimes we even do “sprawls”, where the body doesn’t go to the ground at all as a burpee variant. 
 As for avoiding flexion/extension through the burpee for safety, as a general rule, it’s horseshit. Spinal flexion and extension in this manner is fine for a healthy spine. 

If you keep your butt and belly squeezed, you're actually practicing a good skill by bowing and flexing. On the other hand, if you want to work on the strength part of it you would want to practice the rigid body position. Check out a video called Skill Transfer of the Burpee - it's with Carl Paoli and it's in the Journal and probably on YouTube also.

I call that method of burpees “worming”. I don’t see a problem with it. Consider it a kipping burpee