I agree, it would be convenient and we can already re-copy the data so I don't know why not.
What's the worst thing that can happen?

As for your character actually changing due to being inactive for a moment, that doesn't seem right, perhaps contact the Customer Service, or post about that particularly?

Also a long-shot but have you tried re-copying the character?
I imagine though, that it does show the other character on that page so it would likely just use that again.