Right.
In my case, I was using the nphysics library, which for unsurprising reasons uses Rc for entity handles.
Similarly, in my app's code, I used nphysics' proximity and contact handlers to watch for events that indicated a change in status. Those handlers needed to initialize/set values in a HashMap accessible (and periodically cleared by) the main sim loop -- 'one central thing' that is Rc'd.
It's not sprinkled everywhere in your codebase, and for obvious reasons most libraries don't need to use it. But in applications, a central loop + library-provided callbacks + some Rc'd state of doesn't seem too uncommon.
Learners should read and write lots of Rust. That's a great way to learn what is idiomatic. There will be early missteps, but thankfully the language makes it more comfortable when you do things the right way.
But I would love to figure out how to teach this in a way that doesn't involve random codebases. Some folks learn by doing (I do!), but others fare better with tutorials.
I'm really surprised you think that's the case. Most rust codebases I've worked with use Rc very sparingly, if at all. If a codebase does use Rc there's usually one central thing that is Rc'd, with everything else using regular memory management.
I have noticed that beginners coming from GCd languages often tend to structure their code in such a way that paints them into a corner where they must use Rc. This might be what hit you. I'm not really sure how to teach idiomatic Rust though.