My right to privacy ends when i start engaging in money laundering or fraud not when somebody else does. Otherwise this is a stupid argument because there will always be somebody engaging in money laundering or fraud so there will never be privacy. There's no justification to say "oh well it's possible you're engaging in one of those so we have to remove your privacy so we know. But it's to keep everybody safe/for the children/insert bullshit excuse here so what do you have to hide!"
And bills probably shouldn't be serialized for that exact reason. My right to privacy is more important than anybody's right to feel "safe" from the evil bad guys. The correct answer to stopping crime is to stop crime, not to weaponize our financial system and remove civil liberties.