Well, not neccessarily, this sentence could be said with «мне» too. I think both variants are equally OK.
Thank you for your quick response! My native language Japanese also omit it in this kind of case.
Is this sentence considered polite enough to say to anyone, in Russian? In English, even with the "please" it sounds blunt, and I would use "Could you give me the spoon, please?" instead.
Yes, it's polite enough.
Watching tv with a Russian friend, i saw a scene where a bride at dinner sweetly says "дай мне вананчик" to her new husband. It seemed so blunt but my friend said the diminutive 'чик' meant it was polite, even without a 'please'. It seemed odd. And still does!
Also odd that you can add an affectionate diminutive to a random noun too, but that's for another conversation i guess!
I know from experience Russians generally do not care for overly polite conversations.
Blunt sentences suit them just fine
Everywhere ones don't like blunt expressions, this sentence is polite in russian