NFT's perfectly solve the problem Proof of Ownership, but they cannot solve the problems of Proof of Uniqueness or Proof of Scarcity by themselves. Digital goods are practically defined by their trivial marginal cost of reproduction. What sense does it make to prove you own something that is reproduced and cached automatically in your browser by simply viewing it?

NFTs will find better success with items whose scarcity or uniqueness is constrained by the law or physics. An NFT proving partial ownership of a company like Apple will work because there are legal penalties to copying Apple and it's property. An NFT proving membership in a nightclub will be safe because copying the NFT's smart contract doesn't accordingly copy the physical building the nightclub is in.