I don't chat during live games either. I use up most of my time thinking about moves, if I were switching hands between the keyboard and mouse I'd lose on time too much. After the chat I'll throw out a "well played" or "fun game" depending on how well I think they played, and I'm usually up for chatting a bit too if they want to talk about the game.
In online games I do like to get to know the person I'm playing, but I usually get no response so I haven't been trying to get conversations started as often.
Is it really considered bad ettiquette to turn down a rematch? Usually if I'm playing live I just want to play a quick 20 minute game and be done with it, so often times I'll decline rematch offers.
I dont like to chat because we will lose our concentration on the game.