A profile is a unit, not a picture
The numbers in an image file do not mean anything on their own. A pixel recorded as 255 in the red channel means "the most red this colour space can express" — and how red that actually is depends entirely on which colour space you mean.
The most saturated red in sRGB is noticeably duller than the most saturated red in Display P3 or Adobe RGB. Same number, different colour. The ICC profile is the label saying which one applies.
Strip the label and software falls back to assuming sRGB. If the file was actually Adobe RGB, every colour is now being interpreted against a narrower scale than it was recorded on, and the image looks flat and desaturated.