Maybe Artoo is like Captain Christopher Pike in a way. While his other beeps and noises are computer talk, two beeps means yes and one means no. So when Luke asked and he said “Beep Beep” he was saying yes.
Of course being a machine I would think that the technician would be able to tell if Artoo was in sufficient shape to perform its tasks. Being a bit banged up doesn’t mean useless.
After the death star is destroyed when Artoo is being lowered out of the X-Wing and 3PO is distraught about saving him Luke and the others blow him off and walk away. So it seems Luke may not have been too attached to Artoo in the first place. (Well, it is just a machine, really)
It’s a little known fact, but during the taping of Star Wars Kenny Baker(the dwarf who plays R2-D2 and is physically inside the droid prop) actually said something there. They edited it out of the soundtrack, but didn’t re-shoot the scene. As such they had to leave Marc Hamil’s response to Kenny’s comment in because it would be years before they had the technology to re-work Hamil’s physical reaction to Baker’s comment.
He thought about Anthony Daniels. The inspiration for the scenes in the prequels where he has booster rockets and can fly around came from one time when his concentration slipped and he thought about Peter Mayhew.
Wild-ass guess: After all those years working on his Uncle Owen’s moisture farm, Luke has undoubtedly seen hundreds of old broken-down droids come and go. He’s probably learned to interpret their boops and beeps from maintaining the equipment and trying to keep it all running.
R2 has shown a propensity for expressing various emotions- albeit wordless with his computerlike beeping noises.
Anything from low pitched quick beep to a whine to express sadness to the full on shaking in excitement BWEEP BWEEP BWOO at the end of Ep IV.
I have always figured that Luke didn’t understand R2’s response as words- as much as he understood the expression of emotion that the robot was conveying.
If it comes to that, how did Han understand Chewie, Greedo and Jabba, and vice-versa.? Seems that races in the Star Wars universe can usually *understand *each others’ speech. Not always, but usually. If Han can understand Chewie’s growls, then Luke can understand Artoo’s beeps.
The truth about R2’s beeping and booping is even more insidious. Ever notice how he sometimes seem to go on and on just to say “yes” or “no”? Fact is, whenever he does this, he’s actually saying “Oh, and by the way, there’s something I’ve been meaning to tell you about your father … crap, gotta go fix the hyperdrive. Remind me when I get back, and we’ll talk.”