That is what archival copies and emulation exists to protect. In case your physical copy that you purchased becomes damaged and as a result is no longer usable, you still have the legal right to access the digital content you paid for. You have the legal right to make your own backup copies. You cannot distribute the copy, and are only entitled to one (at a time), and must destroy the copy if you sell or give away your physical copy. Basically the physical copy acts like a proof of purchase.

Nintendo does not know the law and asserts their own creative interpretation is correct, but the letter of the law is very clear.