Many years ago I started this thread https://communities.bentley.com/products/microstation/f/z_-archived-microstation-v8i-forum/86752/ss3---copy-model-and-levels-problem which although a ST was filed I don't think the problem has gone away. In fact I know it hasn't. The problem still occurs in CE and it drives me mad!!
Why doesn't CE remember the levels state and not turn on all levels when copying a model? As I noted in the original thread the problem is mainly when working with .dwg files.