Speakers of (American) English not infrequently start answers to a question with one or another variant of the sentence “That’s a good question.” It can be heard, for instance, in broadcast interviews, but not only. This opening can be annoying to the questioner (or to someone listening/overheating the conversation) because it may seem utterly otiose. However, it does have the multiple communicative effect of: (1) complimenting the questioner for posing the question; (2) informing the questioner that an adequate answer may not be in the powers of the interlocutor, and forestalling a censorious judgment (silently) resulting therefrom; and (3) keeping the channel of communication open withal.
The last effect fulfills the so-called PHATIC FUNCTION, i. e., that of keeping the conversation going. Speech gambits that keep the channel of communication open include not only whole sentences but a range of vocables that are not really words sensu stricto but sounds such as “uh-huh,”hm,” grunts, and even audible intakes of air. These are all (largely unconsciously) meant to avoid creating the effect that one of the parties to the conversation is not listening or not interested in keeping it going. All genuine conversations (unlike speeches or declarations) are embedded in a social matrix, in which mollifying one’s interlocutor is an intermittently necessary goal among others.