I love karate, but these fights are really beautiful. Notice the lack of protective equipment. In the first fight you can see the BJJ competitor using open hand slaps (as well as punches) to his opponent’s head. Toward the end of the video you will see a karate man receiving elbow and forearm strikes to the back of his head and neck. These do not immediately end the fight, the karate-ka continues until he is choked out (note that even powerful, well placed blows do not always result in your opponent being instantly incapacitated).
Rather than dismissing these fights out of hand, karate people should study them. No matter how powerful our punches and kicks are we should assume that we are likely to be closed on. Even punchers like Jack Dempsey, and Mike Tyson threw many punches before landing the “one” punch that knocked out, or injured their opponent. Karate people should not delude ourselves that our experience is going to be that different. It is really difficult to get in that one good, fight ending strike.
Training to both hit hard and deal with the press of a determined attacker who is likely to push beyond our striking range is essential. We should not be naive about ground fighting. At the very least we should include enough of it that we have some chance of regaining our standing position if we are taken to the ground.
Put aside the rhetoric about the superiority of whatever fighting method you practice and watch these fights.