Phonics is memorizing the alphabet and basic syllables as well as learning how to combine them into a spoken word. It's not narrow since phonics is by definition what you describe.
I was considering the distinguishing characteristic of phonics as sounding out a word so you can make an aural association to a word you already know. So rather than memorizing whole words you can memorize some basic syllables and rules to speed up the recognition and memorization process. You can't do that with a logogram script, or if your first language is sign language. (I'm sure remembering and identifying phonemes is still important for deaf children in the context of a phonetic language, but I'd bet it's a more arduous process, more akin to learning strokes in Chinese logograms.)