NFTs solve none of these problems. The underlying asset is not stored on the blockchain and can be deleted at any time. Fakes are unaddressed since you can only validate you are the owner of a specific url and there's no guarantee that what you own is the original version (bytes are easy to copy). Any validation of authenticity must happen OFF of the blockchain in which case why are we doing this again? Transaction costs are a function of the market (even on the blockchain) and are not at all connected to NFTs.