Sorry, you are confused about Suzuki. Suzuki it's a method that was basically designed for kids, (so they can start piano at 4), since they are so little, they start learning by imitation: the teacher plays and then they play. Sightreading is not a priority at this level. Of course they learn to sight read, but this is not a priority at first. The Suzuki Repertoire it's well designed, you follow it but your teacher chooses what other pieces you need to solve your specific problems. Also, you learn to play in Public because tests are in public. There is a good approach. Read more on the internet and you will see. I started with the "traditional"method, but I'm on the Suzuki now. The fact is that there is no a "traditional"method when you have a really good teacher. Suzuki teachers are well trained. And there are others well trained too. Suzuki is very different from Yamaha method.
Best wishes,
Alejandro.