I am using RawTherapee to process images. This program (and I suspect many others) has an option called "Working Profile", which you can use to adjust how the image is displayed; and an other called "Output Profile", which is the profile embedded into the image (this functionality is better explained here).
I believe I understand how color management works, and I am thus very curious why on earth you would need to save a picture with a profile. Aren't profiles supposed to make sure the output is consistent across monitors/printers? If yes, then why would you need a separate complexity level at the point where you save the picture? Aren't the colors simply saved as RGB hexadecimal values, which are then rendered in accordance to your monitors profile?
Similarly, if I look at the properties of my profile (in the GNOME3 settings manager) I get two very confusing tabs. One of them showing an example image looks like "if opened with the profile", and an other one showing what the image looks like "if saved with the profile".
I believe both these examples illustrate this point I do not yet grasp. Again, why would anybody "save" an image with a color profile?