I actually stroke with a fixed elbow for the most part, so I think you would "approve of" my stroke in general. Let me refine what I am saying. If you stroke into air while you are looking at the tip of the cue or at a spot on the cloth where your tip will approach, this is not the same as stroking the cue while looking at an object ball with the intention of pocketing it. You can find stroke errors by practicing into air but that does not mean you won't find others when you are actually hitting the ball. You can stroke into air 100 times perfectly but when you put a cue ball into the shot, I bet most people would find that their follow through is not straight. This can happen for several reasons, including a slightly off-center hit, gripping of the cue at the point of contact, stroking with the cue in a slight arc, etc. These imperfections are not always visible until you have feedback like contacting a cue ball to show the cue going off line and illuminating a problem.
I think the act of shooting at an object ball changes things as well, and may cause swoops or other problems not experienced by stroking into air when your attention is not being occupied by the need to pocket the ball.
I'm not an instructor, but I know what I've seen over the last decade of recording my stroke and looking at details like this in slow motion. IMO, stroking into the air might be enough for beginners but it won't show the full extent of stroke problems. Let's put it this way... Hitting the cue ball and also aiming at an object ball is another way of bringing out hidden stroke problems.
Also, for Scott Lee, there is a typo in your signature. Your link is missing the "l" in knowledge, FYI.