Because your eye sees them that way. Your eyes have an automatic white balance built in that gets fooled when you take a photo out of balance but doesn't get fooled in-hand. As a result, and IMO, all coin photos should be done in a color correct manner, otherwise you're introducing colors that are not on the coin without the context clues that tell your eyes to correct for an introduced color cast through lighting.
I'm with you and understand what you are saying - however nothing replaces viewing the coin with and without the camera at the same time while on the monitor for white balancing. every time I make the settings technically correct it does not look like the coin in hand. It could be my camera needs some type of calibration, who knows? Nothing like hold the coin up against the monitor after the image has been captured and process as a check and balance.
So that's why the color in all your photos is off -- I've been wondering. Human eyes lie under artificial lighting -- custom white balance using a grey card corrects those lies.