First, those not familiar with FTA (Face-threatening act) need to understand what it is. FTA are the acts which challenge the "face wants" of those in conversation. Given that conversations are not one-dimensional (meaning only verbal), a person's face may contradict or support the one speaking, the one listening, or both (through non-verbal communication).
For example, a person who is angry will tend to have a specific tone to their voice and a contorted face which supports their anger. On the other hand, if a person is angry, their voice is "showing" their anger, and their face is relaxed, the listener may become confused given the speaker's verbal and non-verbal communication is contradictory.
Therefore, the problems with not "doing the FTA" is that the listener and speaker can give contradictory messages if their verbal communication and non-verbal communication do not match.