We don't need to wait around for a court to indict a person for "being a crazy homeless person". That's insanely reductive to the point of absurdity.
It's not just implicit -- assault is explicitly a crime, everywhere.
In the US, there is no such concept as “implicit crime”, but, yes, some of those things are just plain explicit crimes.
> We don’t need to wait around for a court to indict a person for “being a crazy homeless person”
If you are going to treat it as a crime, then, yes, it has all the procedural safeguards generally applicable to crime.
They would be arrested based on the crime they commit, such as assault. Then the court would make a determination on their insanity plea.
Adultery and sodomy have been crimes in most civilization of history too. That doesn't mean we convict people based solely on the spirit of the law, nor ignore the principle of innocent until proven guilty.