Remove "Activity" (River) stream from SITE level, but retain for Groups context

My latest question :)

I have been trying to work out how to remove the "Activity" option from the Site menu, but still leave that functionality intact for Groups.

Most simply, it could be by removing the "button" from the top level menu, I suppose.

I have found an old plugin that turned of "Activity", but it looks defunct. I've found discussions like this one about removing the activity stream, but the solutions remain vague (for me). I've read the River documentation, but that's about including things in the activity stream, not excluding them.

Once again, if there was some guidance for getting rid of access to site-level activity (while retaining it in groups), I would be most grateful to know of it!