I feel a bit like a ‘Time and Motion’ man - but one of the aims of Google Classroom is to make us more efficient and save us time. This is how I’d suggest using team Drives and Repository Classrooms:
Create a team drive for each ‘area’ of your department - the English department might have one team drive for Year 9 English, one for GCSE and one for A-Level, for example.
Use it to store any resources that you are likely to use with those classes. Then it's a case of 'training' people to put those resources (and only those resources) in the team drive, not their own drive. This is simply so that they are accessible by everyone in the department and they won't be lost if someone leaves the school.
You could have some sub-folders in the team drive to impose some order - but I wouldn't have too many. Maybe one for each unit of work? 6 or 7 tops. It might be a good idea to agree as a group on the sub-folders you need - and then agree not to create any more. (We don’t want to re-create anything as dysfunctional as the Staff Drive!)
And then, try not to angst too much about the state of the drive! Keep it under the bonnet and try not to look at it too often! Google imagines the drive as a much more fluid thing than in the old days of loads of nested folders.
It's more important to name the documents sensibly so they can be found easily. Again, agree as a department on your method. I saw one tip on Twitter which named each document with a simple 3 letter code for the unit of work, then a name of the document and then the initials of the teacher who created it. You could just search the drive for the unit of work code and you'd find anything you needed much more quickly than going through loads of sub-folders.
And Google, with its new ‘Quick Access’ section, will get better and better at working out what you're working on at the time and bring those documents to the top of your drive anyway - so the structure becomes irrelevant!
More important still, try to train people to use the Classroom (or your department Site) as the interface to access documents. That's a much clearer and easier way to find a document than using the Drive. If you know you used the document in a lesson near the start of term, just go back in the Classroom stream to that period and the document will be there.
The less people fiddle under the bonnet at the Drive, the more likely it is that it will all work properly!
The idea of a Repository Classroom is a really good one. They should have no pupils, but all the people who teach in that department should be teachers in the Classroom.
Think of a Classroom assignment as a lesson plan - Put all the resources you need for that lesson in an assignment and post it in the Repository Classroom. You can fine-tune the resources over time of course but, essentially, they are there, ready for whenever you want to teach that lesson. Then, you just re-use the post in the Classroom you share with your pupils. (Remember, it will create a duplicate in the Repository Classroom, so just delete that straight away and the repository will stay neat and tidy).
It's a great way of sharing resources as a department - or of working on new resources together so you don't duplicate the effort. And, after the initial creation, it cuts your preparation time to a fraction.
You can spend time thinking about the important things such as how to improve the lesson rather than boring time photo-copying resources.