If charged with domestic violence in Michigan, the prosecutor on behalf of the State of Michigan or local city, township, village etc is the party charging you, not the alleged victim. Essentially, the victim is a mere witness to the domestic violence you committed against the people of the entire state, village, city etc.
Let's use the City of Novi as an example. My client is arrested for domestic violence by the Novi Police Department; the prosecutor will either be the City of Novi or the Oakland County Prosecutor's Office. That prosecutor is the one charging you, the alleged victim is only part of the facts and a potential witness for a trial.
If the alleged victim requests the case to be dropped, it can't directly happen because they are not a party to the case. The prosecutor would need to consider this request and agree; that DOES NOT happen, because a prosecutor assumes the alleged victim is simply doing what the client wants or is scared to pursue the case. Even if that alleged victim says my client did nothing wrong, it was a misunderstanding, that statement is likely to be the opposite of what was conveyed at the scene which was the basis of the arrest. Essentially the prosecutor will believe the past statement over the new statement.
There are other ways to get DV cases dismissed, but none of them involve a prosecutor openly dismissing the case on a public record. DV in Michigan is too much of a hot button issue to be dismissing cases; the thought is, what if this happens again and someone is seriously hurt or killed, we can't just be dismissing cases that may or may not have happened. Some prosecutors will simply let the case be set for trial, and if the victim does not show, the case will be dismissed, but at least the prosecutor can cover their butt and say, well the victim didn't show, I could not proceed.