Hi hebele
My teacher is primarily a Viola player, and I've been with her for nearly 3 years. There's no problem with that.
Scales, arpeggios and Hanon are good for developing technique, if they are practised correctly. There are exercises in Hanon that I have done on a regular basis for quite a long time, and I've found them beneficial. They can be boring!
The schedule that was set up for learning hundreds of years ago, works, that's why it is still used in Music colleges etc today. I'm all for playing Pop music, Jazz, Rock & folk (and do so, on a regular basis) as well as the classical music that I mostly study at my lessons. However it can lead you to develop a lot of bad habits... I certainly did in the 30 year period when I wasn't studying Classical Piano.
That said I completely agree that playing the music you like is one of the best ways to ensure you continue playing, rather than giving up.
Cheers