Creating a program for coaching clients vs letting them come with their problems

I saw in one of these questions you mentioned that you shouldn’t make the client do all the work, that you should create a program for them. This is a bit groundbreaking for me. I have been trained by a human-centred approach that says the client has to bring the problem, that the coach shouldn’t lead because then you’re telling them what to do.
That was my training, but clearly, as I’ve been following you from day 1 of your podcast, what I resonate with most is your style.
When my clients come to me wanting to change careers I work with whatever is going on with them. I solve the problems they bring to the table. One program wouldn’t suit everyone as people have 2 different goals….I don’t think.
1) Do you have different thoughts about this?
2) In your 6 week program for example (when you first started coaching) did you also let the client bring a problem to the session that had come up for them but wasn’t part of the program?
3) Is there a formula for making a program for ones coaching business?