"Dynamic rooting" is pretty much not found in karate. Keeping balance and full control of your movement is of utmost importance. Now, in fencing there is an attack called fleche (flaysh). In this move you explosively launch yourself at the opponent with the weapon extended and the body leading the legs. The attack has you blow past the opponent at the end.
The fleche works in fencing as the field of battle is very constrained, a strip only about 4 feet wide. The attack carries you out of range, both from a counter and your own follow-up attack. You cannot score by moving to the opponent's back, coming up behind him. This is very different from real fighting where being out balance/position is very risky.
Is losing your balance a good thing and workable in CMA? The second clip in your post #7 shows a takedown with the guy stumbling a few steps afterwords, similar to the fleche. He cannot follow up and the opponent is free to regain position. Am I missing something?