Poomsae is not for demonstration. It is in some cases for training and in anothers for Taekwondo itself. You may know why I underline this point. Really many practice Poomsae for the sake of demonstration or the appropiate way only for demonstration with no consciousness. I think, it is owing to that they don't or cannot understand the full meaning of Poomsae.
What is poomsae? Poomsae is the established pattern focused on skills that standardized right motions every Taekwondo man should follow in most universal situations.(Ch.49) Thus, poomsae is a sort of training method and its elements are skills; the skills of fighting. Unless you cannot find why those motions can be a good fighting skill it shows that you don't understand the poomsae yet.
is the Poomsae
The essential factors of poomsae
Current Taekwondo Poomsaes