Why is Taijiquan (Tai Chi Chuan) moving so slowly?

The best difinition I come across so far from this newsgroup rec.martial-arts‘s

“The goal of moving slowly is to insure correct attention is paid to proper
body mechanics and the maintenance of the prerequisite relaxation.

“The goal of training is to cultivate a kind of “whole body”
power. This refers to the ability to generate power with the entire
body, making full use of one’s whole body mass in every movement.
Power is always generated from “the bottom up,” meaning the powerful
muscles of the legs and hips serve as the seat of power. Using the
strength of the relatively weaker arms and upper body is not

It also touched on the goal of push hand:

“The goal of two person training is
to develop sensitivty to the point that one may avoid the opponent’s
power and apply one’s own whole body power wher the opponent is most
vulnerable. One must cultivate the ability to “stick” to the opponent,
smothering the others’ power and destroying their balance. Finally,
the formal combat techniques must be trained until they become a
reflexive reaction. “

That is why I don’t understand Push Hand competition, as push hand is part of training curiculum and different schools/styles have different Push Hand routine. In order to benefit from Push Hand training, both have to learn the same push hand routine and from there, try out the different techniques (Peng, Lu, Ji, An, Cai, Lei, Zhou, Koa etc..)