First, isn't the ICC only competent when no other court from another country is?
So, the ICC could be considered the last appeal possible?
Isn't that why it was imagined?
Second, I know very well how difficult it is to be certain that judges are independant.
In Belgium, an important judge in a paedophile case, was removed by a higher jurisdiction (other judges) because he had a dinner with the families of the victims.
The nomination of judges is obviously a sensitive issue. The ICJ has this.
Judges, here, are not competent for cases where they might have an interest to a certain kind of judgment: for instance if family member or a creditor or a debitor are being sued.
If the judge is directly elected through votes from the city or the province, etc.., it might feel accountable to public opinion and that isn't helpful to a fair trial, either.

Raoul