I agree. I have a cousin who does fabulous copies of great master works. She never tries to claim she owns the originals though she signs all her works as far as I know. She is very talented at even matching the colors. IIRC, she frames her paintings and places a photo of the original on the back, with short explanation. Her work is so precise, I asked her first time I saw them if she used paint by numbers canvases. She was not amused.
That's a great way to study & learn from the masters. Some museums let the artists bring their easels in order to paint from the originals.
I believe the purpose of the identifying signature on the copy makes sure that the painting stays identified in the case that it would be unframed, etc.