No, the criminal justice system is a mess as is, and adults/society generally shouldn't need nannies. Especially because such a system would likely be extremely regressive and hit poorer communities much harder.
What if the police focused on 'small' crimes that involved violence or aggression against the person, e.g. domestic violence, harassment, stalking and so on? That is not something to do with a nanny state, and it should not be regressive, in that I doubt poor communities would fail to welcome a crackdown on violence and aggression.
First, domestic violence in my experience is treated significantly more serious than the second two in your examples. I'm not sure it needs to be more aggressively enforced. Which sort of leads in to the second point.
You claim it's not something to do with a nanny state, I disagree. The reason is that harassment, stalking, etc, even modern definitions of sexual "assault" are both cultural and subjective. Some people's definition of harassment includes saying hello, or an unwanted phone call. These
might fit into my definition depending greatly on the exact circumstances, tone, demeanor etc. Some people's definition of assault might be going in for a first date kiss without asking for "consent." Other people would claim that's ridiculous.
The point is, there's a huge swath of grey. In my opinion there's likely no practical way to objectively define these situations for greater enforcement without venturing into oppressive or nanny state territory. So in order to avoid unjustly persecuting people, the bar should be high. Unfortunately, that probably means a fair amount of it doesn't get punished. It's a trade off. The same reason we have "beyond a reasonable doubt" standard for criminal conviction.
Hopefully that explains why I'm very leery of what's meant by greater enforcement.
