GMT,A simple thought experiment shows that CBs and OBs can be aligned in DIFFERENT PLACES on the table, yet have the same relative relationships. Here's an example (to see the pool table diagram of 3 different shots scroll down a bit). If only information from the OB and CB is used to "aim" those three different shots, the same aiming alignment will be produced--but DIFFERENT aiming alignments are in fact required to make all three of those shots. Therefore, one can logically conclude that CTE can't work.
I understand your points, but CTE can work if the alignment and/or pivot are varied based on CB-OB distance and cut angle. The CTE resource page explains several ways CTE can work. Also, CTE does provide many benefits that can help some people improve their aiming.
I think it is important to realistically acknowledge both the advantages and limitations of any system, including CTE. In threads like this, people in different "camps" seem to have trouble seeing both "sides" of the issue.
People sometimes accuse me of "riding the fence." I don't see it that way. I see it as trying to see both sides of the argument.
Regards,
Dave