I'm using Classroom for the first time this semester with the approach mozzadrella mentioned above. I too initially thought it might work the way you suggest, and was initially a bit frustrated with it, but I've now embraced this idea. Honestly, now that I'm trying to work with it more, I rather like it. Particularly with using Classroom to create private assignment repositories as it will make each new class section cleaner to look and manage through the web interface. I also think that it makes things cleaner for student who can now choose whether or not they want this work on their personal profile or not.
This the first semester I'm using classroom, and only really using it to get the private repositories for students. Before I would create a new org, but fork the assignments over to it. Since I didn't do a fork for my first semester though, this brought along all my old pull-requests, which is how I had students turn in work. So I kept pulling along a big chain of past stuff, which lead to some cheating and I just didn't like it for privacy reasons.
Now that I'm using classroom, I do not fork the main org assignments. I just let classroom create the student repositories from the template in the new semester specific org. If I had two different sections of the same class, I think I would keep them in the same "semester" org as well, just for the sake of simplicity. Any changes to the assignments semester to semester I will just make in the main org as a new "release" version or a new repository.
If you'd like to see what I have, I set up a main course Main Course HTC CCIS 1301 which has the template assignments and some general things like course websites for each semester. I will then have semester specific organizations. HTC CCIS 1301 Summer 2017 is my first semester using classroom with private repositories only for student assignments. (I got tired of having to call out copied assignments.) It won't be very exciting to look at, as all the repositories there are private.
As a comparison, my previous semester HTC CCIS 1301 Spring 2017 shows a forked public repository approach without the use of Classroom.
I've learned a lot from the sharing that others have done here in the community, and I still feel like there is so much more potential for this that I have not yet touched. I'm hoping to embrace more of that over the summer to share with the other instructors at my own institution, and if I get there, I'll share with the community here as well.