This would be very helpful because the palette of colors rotates out. I’d like to quickly select colors that are on a board already with an eyedropper. 

Hi! If I’m reading your question correctly, you can already do this. When you select a color, scroll all the way to the bottom of the colors list and click the “+” icon to bring up a color picker.  There is an eyedropper in the lower lright hand corner of that and if you click it you can select colors from anywhere on the board including images.

I agree it would be better if there were a less scroll-y way to do this with either a dedicated tool or a keyboard shortcut.