Case status "status class" - what is it used for?
If you remove it, then how would you close a case? It won't recognize the Change Case Status activity as actually closing the case.

If you want relationships to exist outside of a case then you can use regular non-case relationships. That's really the only technical difference between roles and relationships. And relationships can still have start/end dates if you need to record that.

And you can still see regular relationships on the manage case screen, under the Other Relationships accordion.