CC has many problems, BUT it never 'kept itself in sync' with the Calibre Library. You had to take action. Choose what books to keep on the device, Then and only then, could you (manually click) Sync, to keep those updated.
Now, If you just want to get books ONTO your device:
USB works (you still need some sort of EBook viewer)
The Calibre Content server (running on your Library machine) allows you to use the browser on the TAB, to read (connection must be maintained) or Downloaded for later use with the Viewer.
Hopefully your viewer has some sort of useful shelf manager (That was what I use my ancient version of CC for)
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