Tonic sol-fa is a non-notation form of notation. It is a learning by ear based approach and learning tones and tonality of the key rather than just reading traditional notation.
Here is an example of Tonic sol-fa compared to regular notation. Every pitch is assigned to one of the Do Re Mi Fa So La Ti Do's. Every A is 'so' and every D is 'do' wherever you look.
It would not be useful because it is not commonly used. It is useful because you don't have to learn all 12 keys, you only have to learn the Do Re Mi Fa So La Ti Do, and learn the pitches of every key rather than learning the note names.