It all depends, if the extra digits were functional I'd want to keep them. I'd be bummed if I grew up and knew that I'd had two extra usable fingers that had been lopped off without my consent. Smaller fingers with reduced function though, they can go.
On the subject of extra arms and legs though, those are usually due to a parasitic twin, where two fetuses began developing in the womb as twins, but one twin somehow absorbed part of the other twin, leaving only the limbs of the parasitic twin remaining. This is much different from polydactylism and people typically do not have control over these extra limbs since they belong to the twin and will not be properly linked up to their nervous system. The little girl you posted the picture of was born in India and she has a headless parasitic twin. Nowadays parasitic twins are usually removed since they can cause heart issues, due to the heart having to pump blood to these extra limbs.
I'm sure Fletcher is good and creeped out now. :)
