Of course. Only staff could see the link while the rest of the users could only see the link to the post history for their own posts. For posts that don't belong to users, the "Last edited by" would simply be plain text.
I think that set up becomes quite a bit more complicated, and since teh Post Edit history is more or less designed as a moderator tool, it makes sense to keep it the way it is right now. You may be able to modify it with permissions / display to change it so everyone can view edit histories.