But shouldn't you also be abe to get that orange colour by adding finely grated carrots towards the end of the cooking? It's a pretty intense colourant after all.

No, it doesn't seem to work that way. Instead of melting into the rice, you just get grated carrots mixed with rice. Which is fine, it tastes the same and the girls eat it the same, but it's definitely detectable to the untrained eye.