Hi,
I grew up with those method books and my teacher back in the day was rather traditional and wanted me to finish the whole book before moving on to the next grade. The whole process was rather slow and quite frankly, probably contributed to my disinterest in piano lessons when I was young. Also, she was a bit averse to teaching pieces outside of the method books. She'd usually tell the students to learn pieces they like in their own time.
I'm taking lessons from a different teacher now. What I find different in his teaching method is that we discuss and choose a piece from each period (Baroque, Classical, Romantic, sometimes Modern) that is within in my level (he prefers original compositions, not watered down arrangements). If I do well on Bach piece, for example, he'd assign a more difficult Bach piece. If not, he'd assign a Bach piece that is of equivalent difficulty to the one I took. We keep doing this for each period.
What I like about this approach is that I'm involved in the building of my repertoire and it keeps me motivated to finish a piece. I too would often work on a piece that is way above my level simply because I love the piece. When we get to that level, I'd surprise my teacher by showing him that I'm already familiar with the piece and we could simply focus on polishing it.
I guess what I'm trying to say is that don't be too overdependent on method books. If your teacher is open minded enough, try learning the pieces that you like (from the method book or otherwise) and making sure they sound really beautiful. As my concert pianist friend would often remind her students, it's quality of the music that counts, not quantity.