So here is another case of a well executed poor decision.
Billy's choice of shot was like having the quarry surrounded and then pulling off the guard to the back door and telling him how to escape.
By removing the threat of the nine ball, Billy has given EF an easy escape route. In addition he has allowed EF in the execution of his own shot to now manage to free a few balls on his own side of the table thereby neutralizing the playing field. (I agree 100% with your analysis, Billy actually weakened his position with his choice for the exact reasons you brought forward)
Typically, balls located along the bottom rail should be considered belonging to both players. One of the main objectives for setting traps in One Pocket is to get at least one ball on your side rail and another on the bottom rail. To have multiple balls on either rail adds to the navigation difficulties for an opponent when he becomes trapped in the stack. Billy removed a critical ball from that equation. Bad move.( That's what I just said:lol)
Someone, forgive me for not remembering who, suggested thinning off the six ball and playing the cue ball two rails into the side of the stack. This is the right idea but in my experience this requires great skill to make such a precise carom. In my opinion it is far easier to find that precise angle and speed with the use of an intentional scratch. Now EF is in a far more potent trap, one from which he may find a temporary haven somewhere, but regardless of where he leaves him, Billy will be in a far better position to strengthen his hold on EF.
The red line in the image shows what I call the catchers mitt. I am always looking for simplistic ways to put my opponent in the web of this mitt, particularly when I have balls on both my side rail and the bottom rail. And I'm not fond of having to remove any part of my trap to accomplish this task, especially when I have other paths to the same cue ball position.
BTW; anyone who has not developed a good feel for this particular type of kick shot is not yet a One Pocket player. This shot is one of the more common kicks in the game and must be an arrow in the quiver of players of all skill levels. If you don't know it, learn it!
Tom