A melody or a lyric is not like an API. A musical note or an alphabetical letter is. To take your own example, "For example, I can play "Yesterday" on a piano, guitar, speak-and-spell, and it's still a Beatles song". The musical notation is the API, and you are able to implement the copyrighted melody via that API on a variety of different instruments. Imagine if somebody held the copyright to the API and only allowed a guitar solo to be performed on a particular brand of guitar? Would music be where it is now?
If you allow an API to be copyrighted then you will destroy a good amount of the software industry. Designers already do lock down APIs when they want to, even 'open' APIs such as Google and Facebook require you to generate an API key which they control the validity of.
It should definitely NOT be copyrightable. It would be detrimental to both industry and society.