... how do you gradually increase the difficulty or gradually add new ideas?
It is not that complicated. Just let the student decide what he wants to play. The worst case scenario is the one where the student is a child who has been brought to you because the parents want him/her to play but s/he is not at all interested. You then have to decide if you are going to take the child or not. If you do, then you will have a lto of preliminary work to do (= musci apreciation) before you can actually do anything really meaningful.
Someone has ordered the ideas for me. I like that. I would think I was leaving something out without the method book.
Then perhaps you should use method books. I don´t like that at all. And in general I disagree with almost everthing in the method book. So I don´t use them.
With just using pieces, how can you look at so many to know the student is having a challenging, but attainable, step? And then with a lot of students...
Er... it is usually pretty clear after a couple of lessons if the piece he has selected is easy, challenging difficult or impossible. If it is not easy or challenging, then a different piece must be chosen. Sure this will require a teacher that knows a lot of repertory. So, start collecting pieces. The forum has already hundreds, maybe thousands of graded pieces that have been suggested over the years. Stop pussyfooting around and get to work!

I would guess you have a large list of pieces, graded by difficulty, and then you would have prepared speaking for the concepts they need to cover. Instead of the method book, the student goes through a path of pieces. Is that it?
No, that is not it at all. A piece is selected not because it covers this or that concept, or because it will develop this or that technique. The piece is selected because the student would love to play it. That is it. Nothing else and nothing less. Now, in order to be abel top paly the piece s/he will need to address certain concepts and techniques pertaing to that piece, so one addresses them. Technique and concepts are addressed on an "as-needed" basis. They do not guide the choice of repertory. Love for the piece guides the choice of repertory. The choice of repertory guides the concept/technique acquisition, not the other way round.
What about a theory book? I would also think that a teacher teaching without method books might be doing more theory and ear training anyway though.
A theory book is useful as a reference. It is also useful as material that the student can tackle on his own without need to waste lesson time for that purpose. Most theory should be learned in relation to the piece, by carefully and thoroughly analysing it. Again theory material is not provided on an emptly context (the logical method) but on an "as needed" basis in accordance to the piece requirements. Some teachers get scared that the theory knowledge so gained will be "patchy", but this will only happen if the studnet learns one or two pieces. By the time he has 20 pieces in his repertory (with my studenst this means 3 - 6 months), they will have covered most of the theory by simply analysing the pieces. And they will never forget it, because the knwoledge they have been imparted has
meaning for them.
What about the idea of using a method book and other pieces? That's what I tend to do. I like how the ideas are already planned out and "baby stepped" in the method books, but they need some extra pieces, not just the method book.
Thankfully, piano teaching is not a regulamented profession, so you can do whatever you want. Personally I think it is a waste of time.
I think I'm getting blurry on what "teaching with a method book" is and what "teaching without a method book" is.
Then you should try this experiment. Choose 3 students and teach them using exclusively method books. Follow the book strictly. Then with another three students, just use the repertory. No method book at all. Make sure the 3 students of each groups are similar in respect to everyhting (phisicality, piano experience, etc.) so that whatever differences you may observe both in your students and in yourslef while teaching one way or the other can be traced mostly to your teaching style. After 6 months, compare results and tell us about your findings.
Best wishes,
Bernhard.