Yes, it is silly. Stripping these is about as trivial as removing "this post was written by Claude" appended in plaintext. You could make a clipboard monitor that does this as soon as you CTRL+C, it's a 1-shot prompt. Not to mention that these wonky Unicode chars will break in every other program.
Stripping Anthropic's watermarking, however, is more difficult - probably about 2 prompts.