I think it mostly depends on what you are referring to as an Operating System.
Dos and Prodos are Disk Operating Systems.
All the things you mentioned, sound, graphics, keyboard, text-screen, printing, memory management on newer systems as well as old, require drivers. They help make a user interface, but I don't believe they are necessary to make up an Operating System.
Part of the reason no master system that handles all of these activities has ever been written for the Apple II, is mostly due to the lack of memory, especially on the II or II+. And it would be very hard to tie these things to multiple programs and still leave room in memory for the program itself. Plus there is the argument that each program would not be unique if there was a standard for, input and output. And not all activities need to be in memory at the same time.
Basic.system, under Prodos, handles some of these activities. It handles keyboard input and output in specific ways, and Prodos handles interrupts that can be programmed to handle some of the other activities mentioned, mouse, sound, printer.
For the text screen that is only 40 bytes wide by 24 lines, who needs a driver? And with applesoft support, printing to the text screen can't get any easier than; HTAB 10: VTAB 10: ? "HELLO WORLD!".
Or output to a printer. PR#1 (or 2) is all that is needed to get a printer going. For basic printing, who needs a driver? For graphics printing gets a little more complicated and a driver is only loaded as needed.
As for graphics, lo-res and hi-res are somewhat supported in applesoft, but the real power to use graphics in a GUI requires the use of Fonts and fast block shapes and Applesoft only supports using vector shapes.
The only real difference between Apple II OSes and modern OSes is, that drivers are only loaded when needed, where as on modern machines they are mostly just all loaded at the same time. Which all just comes down to memory availability.
Of all the things that the Apple II has to offer, and in some ways the greatest advantage it has to offer is its ease of use, to get some activity working without the use of complicated drivers