The bike in the first video gets out of attitude when the front wheel returns to the pavement. The trail does not get to do what it is designed to do, when the front is light. Not such a big problem at slower speeds.
The trail on sport bikes is less to help with quick turning. Many have steering dampers. That is the type of bike newbies keep asking if it is okay for their fist bike. But a newbie would never ride in a non safe manner, just like the guy in the video.
The wobble and weave video narrated by Murray Walker, is fiction IMO. Given that I never heard one report of it happening. I ride one of the bikes shown in the video, and have been on others.
All of that era of bikes were raced in production classes at the track. Zero reports of wobble and weave.
Later when the horsepower was a bit much for the frame, we had flexible flyers. Read Reg Pridmore's book.
I'll bet his seat was a different color after that.
Mine would have been.
My '99 Goldwing would do that if you took your hands off of the bars...but not while holding the bars.
Turned out to be the tires. Bike had Dunflop E3 on the front.
Changed to a Michelin Commander II and the problem vanished completely.
I realize that this was different than the video. His shake started while he was
still holding on tight.