I know this is an oldish thread. I don't come on this forum often.
My son learnt via the Suzuki method for about 2-3 years, then we decided that I would continue to teach him (teacher moved.....difficult to get to). I've also taught a few other ex-Suzuki students when another Suzuki teacher gave up the 'job'.
Yes, they do learn to read music in the Suzuki system, but it's secondary. Rather like how we first learn to speak, then a few years later we learn to read.
My son reached about a Grade three playing standard before he was taught where middle C was. I found it fascinating, but I can understand 'traditional' teachers being shocked
He reached about Grade 7 standard when he was 11, and by then could read as well as my other grade 7 students, and boy, don't I envy his ability to learn things by heart so quickly. Just a couple of play throughs and he's got it. He also has a good ear and can work out tunes without the music much quicker than most.
Another thing was the high level of technical training he had with the Suzuki method. As no lesson time was needed learning notation, and pieces were played over and over again, there was plenty of time to work on how he should hold and move his hands, posture, getting a good tone etc.
Watching his lessons, and those of the teachers other Suzuki students was a great learning opportunity for me. I was amazed at how able these children were. 3-4 year olds playing little Bach pieces with great technique. They weren't even allowed to go onto book 2 unless they could play the whole of book 1 (which is far from easy), by heart effortlessly.
I do believe that if you take on a Suzuki child, you need to really look into the system and understand it. The pros and cons. It's not like taking a child from Thompsons to Piano Time. It's almost like another subject completely (in the early stages anyway).
I also believe that when it comes to teaching a Suzuki child to read music, you have to be extra vigilant. As they are so aurally strong with good memory skills, they just don't get the practice in reading notation that others get. For example. The average non-Suzuki child gets a new piece, works out the notes, keeps their eyes on the music for at least the first few times of playing (if not forever). They are constantly reinforcing the note reading part.
An ex-Suzuki player will learn to read the notes through, maybe just the once, and they will then rely on their memory and aural skills the second time around. It's easy to think that they are good note readers until you catch them out by asking them to go from bar 34
And of course, the playing is much further on than the the reading. As they usually start so young, I like to think that they are ahead with the playing, rather than behind with the reading

It's tough for them to have to go back to the simple tunes when their playing is so far advanced. After all, they hardly ever do really simple tunes even at the start (once they've moved past the million Twinkle songs anyway)

What I did to help them with the transition from Suzuki to traditional was to continue to hear them play their Suzuki pieces, but spend the other half of the lesson working through my normal method books. The Suzuki pieces are lovely. It's a shame to abandon them completely.
When I worked on the method books of my chosing, I moved them fast. So it was 3-4 pieces minimum a week....usually more. I may have needed to pull out loads of other methods so it wasn't getting too hard too quick, but the idea was that they were continually having new pieces to read and the pieces being changed as soon as they showed signs of memorizing.
We still had a piece or two that they would learn close to perfection, which they automatically memorized, but a fair bit of time was spent just sight reading fun pieces.
All my ex-Suzuki students now read well and have also managed to keep their aural and memory skills thanks to their early training.
I must admit to really enjoying taking on these kids, though I would always encourage them to stay with the Suzuki method if possible had they started with it. If they can't for various reasons, they are a joy to teach if you teach them with an understanding of their method. For one thing, they don't get to do anything modern. They go crazy when I give them their first jazzy pieces and a Christmas carol

Also there is usually very good support from the parent as the parent learns how to teach their child the Suzuki pieces from the start. It's a partnership between teacher, parent and student.
sorry it's long. Hope there's something there to help.