I'm setting up my Windows 10 Style Start menu, and I'm setting custom icons for many of the tiles. Once a custom icon is set, the icon's color can no longer be changed. I'm guessing the reason for this is that you can't see the color if you use an icon without transparencies. However, if you use an icon that does have transparencies, the background color is still visible:

The background color is purple on the left, and grey on the right. So the only way to change the color once an icon is set is to clear the icon, change the color, then set the icon again.
Given how common it is to find PNGs with transparencies if you google an application's icon, I think it might make more sense to just always leave the color context menu entry enabled.