With paste you can see what got pasted, so you've got a chance to realize it is not what you wanted.
But how about for copy? If you meant to copy into register 'r' but missed by a key and typed 't' would it be noticeable right away?
I don't use Emacs so don't know how its undo works, but when I use named registers in Vim it is often to hold something that I'm not going to paste for quite a while. By the time I notice the error it would be annoying to undo all the way back to the mis-copy.
If copying into the wrong register was common enough to need to be addressed, my first thought would be something like adding a status message pups up for a short time near the cursor that says something like "Copied to 't'".