It's often not the person pressing charges, but the state pressing charges because of the harmful effects the illegal acts have on society and the potential harmful effects on others were the illegal acts to continue.
This is also why they still charging rape even if the victims didn't feel 'threatened'. The acts they described fit the crime of rape (yes even in the UK), so them not being 'threatened' by it is irrelevant. I might not feel 'threatened' by a pick pocket, but that doesn't make it not theft.....
I think we understand the concept. In the U.S., too, the prosecutor acts on behalf of the government, not the victim. But in the U.S., if the victim subsequently says "It was just a misunderstanding" or "I was angry, he cheated on me" or "I won't testify," that's pretty much the end of the case. In Sweden, can the victim be compelled to testify? Can her initial report to the police be used at trial by itself? Can the defendant be convicted without the victim's testimony? (In your example, if you decided that to avoid the hassle of testifying against a pickpocket, you might "remember" that you dropped your wallet or left it somewhere.) If these women say "The guy is a jerk, but I'm not sending him to prison," can the prosecutors pursue it anyway? Related question: Do Swedish criminal trials use juries, or is the verdict determined by a judge or panel of judges?