No. No one gets shut down. That's how freedom works. That's how Liberty works.
Although Rittenhouse is free to sue the media, but that's has an even much taller level of prosecutory evidence than proving murder, let alone manslaughter.
By default, the media can say what it wants, evne if harms someone, less the prosecution can prove willful harm. It can even extreme harm, but if it is not proven intentional and in spite, the media can do what it wants.
I hate it too, but it's what the 1st Amendment is all about, as much as it's abused.