“The right socket” can only be implied one way when talking about a body just like you only have one right hand despite the fact that it is on my left when looking at you.
If you are facing a wall-plate with two power sockets on it side by side and you are telling someone to plug something in, which one would be "the right socket", and which would be "the left socket"?
If above the wall-plate is a photo of a person and you are someone to draw a tattoo on the photo, which is "the right arm" and which is "the left arm"?
ETA: and if I were telling someone which socket to plug something into, it would absolutely be from the prospective of the person doing the plugging, not from inside the wall.
"Right hand" is practically a bigram that has more meaning, since handedness is such a common topic.
Also context matters, if you're talking to someone you would say "right shoulder" for _their_ right since you know it's an observer with different vantage point. Talking about a scene in a photo "the right shoulder" to me would more often mean right portion of the photo even if it was the person's left shoulder.
