I think the idea is that the victim's testimony is often central to the case. So if they refuse to testify, or say in court that everything is fine, then it's likely the case falls apart. So whether or not they can technically prevent the case, they can often effectively prevent it.

More detail: https://conncriminaldefense.com/blog/how-do-you-not-press-ch...

No, it's correct. I've been involved in several incidents where the police asked if I wanted to "press charges" against the offender. For minor incidents this greatly reduces caseload while giving me the opportunity to ensure I get justice.

Prosecutors have the option of pressing charges on behalf of their jurisdiction for criminal cases and can sometimes do so even if the violated party declines to press charges themselves.

Assuming you're talking about the US, you're slightly mistaken. The police just use the phrase in the colloquial sense, as a way of asking if you'd co-operate with a prosecution. The actual report gets written up then goes to the DA's office. The DA's office ultimately makes the call. Your cooperation is a big factor, but it won't force their decision. A private citizen doesn't have the authority to force the DA to bring charges if the DA decides it's not worthwhile.

In Germany there is "Antragsdelikt". Such an offense cannot be prosecuted without a complaint by the victim.

https://en.wikipedia.org/wiki/Antragsdelikt

Interesting, this seems in principle to be similar to a (hypothetical) concept of "prosecutable torts" in English Law, indeed some of the examples (trespass to land, defamation) are torts in English Law.

If your witness refuses to cooperate, the case is often dropped if they can’t get a conviction.

When cops ask “do you want to press charges” what they really mean is “are you willing to follow through with everything if charges are pressed”.

You’re correct. Charging decisions are made by the DA/US Attorney and not the victim.

Colloquially, the phrase usually means that the victim will not participate or cooperate willingly. It makes a case harder to prosecute in many cases, and is a big issue for domestic violence cases in particular.

This depends on the country. In Canada it is not the victim's choice.

Certainly in the UK it's out of the hands of the victim.