Is it ok if the letter to your pen pall is ended with "Well, I'd better go now as I have to do my homework / Keep in touch"?
It seems to me not polite. Is it?
Why do you think it's rude?
Would "I'll keep in touch" or "Let's keep in touch" make you feel better?
The phrase "I'd better go ..." seems a bit rude to me because if the person is so busy, why does he write the letter? Shouldn't he choose a better opportunity for writing letters? I mean when he is not in a hurry.
"I'd better go now" is a frequently used phrase to mean: time for me to end this conversation.
It is very informal and used all the time in casual letter writing.