I think the jury is still out on the back leg drive. Opinions vary from just a nudge with the inside of the leg to tip the center of gravity toward the target to a full-blown push-and-drive. 5 different instructors can look at the same video/pictures and draw different conclusions. That’s probably a topic for another thread.
What I do feel safe in saying though is that a pitcher whose initial move is away from the target, or at least not toward it, will feel and need more engagement in the back leg. The back leg is the only thing that can stop the rearward momentum and begin the redirection to the target.
I personally would rather see drills that encourage the hips to move toward the target as the leg is coming up rather than the distinct pause or vertical “posting” that these drills seem to encourage.
I will say tough I do like what the kid in the drills is doing with his stride leg. Driving the knee toward 2nd base as the leg comes up puts the hips in a powerful position for the move to the target. If that is a result of these drills then that is a positive outcome.
I think with a little tweaking of the drills though the initial movement away from the target could be eliminated. In the video on the left the rearward movement could be eliminated just by starting with his feet closer together inside the width of the shoulders. This would essentially be the same as the narrow stance drill I mentioned above.
In the drill on the right I’d experiment with the position of the chair to see if I couldn’t find a location that encouraged the same leg/hip movement but didn’t require the initial move away from the target to maintain balance.
In getting back to the OP I agree that better engagement of the hips such as shown in these drills would be a good place to start.