Because in the US (at least) if the victim won't press charges the police can't take action. And in a case like this the defence will attempt to attack the (alleged, at the time of the trial) victim's credibility, which can be devastating. It's the main reason why rapists so often get away with it. Also why gang members are hard to convict.
Some crimes don't have a legal victim, e.g. murder (victim is dead) or so-called "victimless" crimes (prostitution, drug possession, speeding, etc).
That's not true. The decision about whether to press charges is up to the prosecutor. The prosecutor will often take the victim's wishes into account when deciding what to do, but they aren't required to.
Kidnapping in the the latter category it does not require anyone to press charges. Assault is the same way as well. If LE has evidence they can move on it. The fact of the matter is prosecutors don't want to risk their win loss ratio.
Some crimes don't have a legal victim, e.g. murder (victim is dead) or so-called "victimless" crimes (prostitution, drug possession, speeding, etc).