In this particular setup, I expect that many lower level players would play the four first. This isn't necessarily because they don't see the better pattern, but because they get nervous when the path to the pocket requires that the OB pass relatively close to another ball.
In your scenario, you didn't show where the opponent's balls are, or where the eight is. I can think of many scenarios in which I would play the 4,7,3...it is an extremely easy pattern, depending on obstacles.
I agree with your first point. Immediately after that game, I pointed out to him what shot order I thought he should have taken and why. I suggested practicing the shot for the very reason you mentioned, so he could become comfortable with it. Do I think he remembered my suggestion and practiced the shot? Not really.
I did not videotape the match. But from my recollection while there were a lot of balls on the table at the time, the scenario was as straightforward as shown in the picture. My picture was only provided to illustrate the level of simplicity I wanted in these patterns. There will be other tactics to add to his skill set later that would enhance his play. But for now, I would be happy with modest expansion of his skills. He looks at every situation as a blank slate. When there is a full table of balls, he cannot readily grasp his key issues and set a strategy. He spends so much time thinking about every possibility for shooting his seven object balls, that he has no time left on the clock to think about making the shot.
Thanks for your comments. I really appreciate the responses.