Assuming the only evidence for physical assault isn’t just the victims statements (but even then), I feel that both crimes are currently being ignored.

To go back to the example of Germany: If you accuse someone of a crime (directed against your physical well-being or property) here, towards authorities (e.g. police) and then say “but I don’t want to press charges”, that no longer matters - they are obliged to record a report of a potential criminal offense and leave it to a judge to decide on how to proceed.