I studied American-Korean TKD.
Your set of questions are interesting in that they place importance in the style of the techniques taught. In the association I was in the greatest emphasis was placed on developing the mind, though the physical aspects were not neglected.
Situational awareness, self-control, mental clarity, confidence, tactical skills and focus were the most valuable things I learned. These skills should be common between and equally transferable between different styles.
I noted that entrants from different styles blended into our association well, as American-Korean TKD was a "non-traditional" style. For instance, the instructors were interested in, not dismissive of, the classical American wrestling techniques I employed in our groundfighting sessions.
As for the bowing and rigid protocols: I found this was very helpful in developing self control and respect for position.