(Not all of which necessarily apply to Polanski).

Crimes against children. Who speaks for the child? Her parents? What if they are the abusers?

Prevention of further crimes. If you put a child molester away, despite the wishes of either the child or the family, you may prevent further children from being harmed. Especially if registry as sexual offender is required.

Equal justice for all. If you allow some perps to settle with the victim in civil cases, you advantage certain perps and also certain victims compared to others. Some perps are more likely to be able to buy there way out: why should they get off compared to others. There is nothing that prevents a victim from winning a civil judgement if the perp is found guilty of criminal conduct, and it probably makes it easier for victims from backgrounds whose access to quality legal representation is impaired compared to other victims. Yeah, contigency, ambulance chasing, etc, but still.

Mostly, allowing the victim to decide whether to press charges is at the discretion of the authorities. It is more likely to happen when the crime is very difficult to prove without the victim's cooperation, or when the crime is petty, or when the crime is unlikely to be repeated by the offender against others (personal feud, etc).

My bet in the Polanski case is that (assuming he is extradited) he'll make a new plea bargain under slightly less favorable terms than before. Only a guess.