If you watch The Original SW Lucas knew when it was time for comedy and time for drama. Just watch the ObiWan/Luke talk about Lukes father in ObiWans hutt. Right before it gets to the key conversation in the movie, C3PO says, "If you don't need me anymore sir, I am going to shut off for a while." That is Lucas understanding in 1977 that we don't need to hear annoying C-3PO while Obiwan talks about the force, the lightsaber, and Lukes father being killed by Vader.
Honestly, even if 3PO hadn't been shut down at that point, I don't think he would have said anything. It's not in his character, especially not in the first movie. He knows he's a servant. He wouldn't start spouting off whiny, prissy chatter at a somber moment, just like he didn't say anything when Luke was grieving over Ben later on. The droids just watched with sadness, and R2 gave a tiny whine. But like I said, especially in the first movie, he wouldn't have gotten in the way. In the sequels, where he got more tinny and whiny... eh, possibly. In the prequels, he probably would have said, "That's whack!" or some other pop culture phrase that's totally out of place.