Can you describe some more about how you are using the stage object to render multiple camera shots?
In any case, to allow saving .cxr in the render settings, we'd have to be able to save it in other situations as well, like if you have a history of renders in the picture viewer. But in the latter case, the data needed for .cxr is already lost. This means that we'd need to make some more changes than simply implementing the saving functionality.
So, eventually, we'll implement it, but there's no plan for it right now. In the meatime, maybe we can find out another way to do what you need. Alternatively, you should be able to use the new autosave functionality that is planned in the nearest releases.