Most piano 'students' learn some sight reading, and more difficult sight reading as they progress through the Grades. What Grade has DD got to, and how much Theory has she done, or does she understand?
But VERY few learners can play 'by ear' without printed music to fall back on.
So 'reading' is good if they want to play Classical music, 'standards' or Musical Shows. But if they want to play Jazz, or improvise or even just embellish the music they are reading, then an understanding of Theory, Harmony, all Scales and Modes etc is required.
Some of the VERY BEST musicianship, reading difficult 'charts' but also improvising accurately is to be heard from the Dave Arch orchestra (Strictly Come Dancing) or the Jools Holland band. These are some of the top musicians in the country (if not the World) and they 100% accurate 'readers' but also creative improvisers.
So, ideally an all-round musician needs to be able to do both - reading scores, but also improvising when appropriate.
If DD studies Theory, Scales and Harmony and really gets to UNDERSTAND music, then she may not even need a teacher.