The doctors argue that legalization of the mild forms would present a balanced compromise for immigrants who believe the practice to be integral to their culture and in addition, would protect girls from being subjected to extreme forms of genital removal in underground operations.

There is no reason to believe that this would effectively reduce the number of people who would pursue more extreme forms of the procedure. That option would already be available to those who seek out 'underground' doctors, and not being selected as an alternative to the more extreme measures.

I see you are comparing male to female circumcision. That is fair comparison perhaps, but it does not work to argue for female circumcision - it may be the fact that male circumcision is also unethical. It is not helpful to you, we are discussing what is ethical, not what is legal (there are arguments that these two are not always the same thing).

Finally saying that some religions or cultures tolerate such practices does not make it ethical. Unless you intend to argue for cultural relativism, it seems an ethical stance can be taken against some cultural practices.