It is not widely appreciated that Taiji, if trained accordingly, is fundamentally a martial art. This misunderstanding is largely rooted in the misconception that all Taiji practice is very slow and 'relaxed' and therefore cannot be at all practical. Most practitioners however, are only interested in the (non-martial) heath and well-being aspects of the art, and this is fine.
For those who wish to apply Taiji in the context of a martial art, it requires a very thorough background in the solo exercises and partner training, before introducing the strategy and tactics of martial practice. To rush too early in one's study to "try and make Taiji work" as a martial art will usually result in abandoning the Taiji principles entirely for the sake of speed and power, or go the opposite way into something 'floppy' and ineffective.
If you are attacked fast, then you must respond accordingly. In the Taiji classics the principle is "If he does not move, then I do not move. If (I sense) he is moving, then I move ahead". This principle describes the importance of awareness and timing.
When functioning as a martial art, the principle is that Taiji should aim to replace raw speed and power with awareness and timing, and a synchronised, highly efficient, whole-body movement. The mostly slow practice of the Taiji forms and partner exercises gives the mind and body time to build a correct physical structure, and then develop the synchronisation and timing by re-training the awareness and fundamental movement skills from the ground up. It is necessary to train slowly at first, in order to develop these skills and create new habitual reflexes.