Sorry didn't see the post, ribbit.
In todays game, I don't think there is any set system per say. A good coach will have his selected charges play whatever is suited to their skills and abilities.
Did Sven use a Swedish system for England ? Did Big Phil use ah Brazilian system for Portugal ? No to both. You choose to play a particular way(style) based on what you have and/or what is required to defeat your opponents. Or so I think. Therefore the coach biggest job, is selecting the best players that he can adapt and train to ensure the domination of his opponents. So it about knowledge, of the game, players and opponents.
So to give my personal answer to your question.
I would like to see a T&T coach,who is able to utilize and consider the advice of experienced international assistants(foreign or otherwise) who are familiar with the opponents we must face. Thus ideally, a T&T coach, Mexican, US, Jamaican, UK assistants - UK as we have a few 1 st teamers there.- all with a particular/specialized area of expertise...
I don't know if it will solve problems or even create some, but I think it is an experiment we could chance only at the beginning of a 4 yr campaign...