Lots of great comments on this thread. Especially Lou's first observation and sjm's contribution on conceptualization and the mental aspect.
One opinion that I'd like to contribute is that while the 'stroke' is important, I think the capability to aim for the various shots accurately supercedes it by a significant margin.
Both are needed of course. An appropriate metaphor might be that the stroke is the pedals and the aim is the wheels of a bicycle. Take the wheels off and you can't go anywhere, take the pedals off and you can still get where you going, just with a little less power and control.
The biggest thing I've learned in billiards, and it took me 15+ years and a lot of frustration, is that I assumed my aim was much more accurate than it really was and hence I falsely accused my stroke of being the cause of nearly all misses. I know there are a great many players still making this error in determining the cause of their misses.
Yes, the stroke can be the cause, but I think it is more likely to be so when one is in the habit of aligning lazily / inaccurately often, in which case swooping and bridge hand movements become a staple of the player's stroke technique.
Work on a consistant straight stoke does have the advantage of forcing the player to align with more precision. So I think a lot of stroke training has its greatest benefit in that it forces a player to pre-align with greater accuracy. Most players are quite capable of stroking straight enough to make most shots with reasonable accuracy, however, most players don't align with near that same degree of accuracy. Hence they post-align, meaning they change their alignment during the stroke via swooping or bridge hand drift during the stroke such that they get closer to the required shot line.
Colin
