Why do some accessories work with the Lightning – USB3 Camera Adapter while others don't?
Yes, there are drivers in iOS. iOS is based on Darwin, the same as macOS. It is the exact same type of drivers.

No, these drivers are not baked into the firmware of the camera adapter. The camera adapter itself does not have specific support for storage devices, keyboards, cameras, ethernet adapters, MIDI keyboards or anything else that you would like to plug in. Those types of drivers run in the operating system on the iOS device itself.

A place to start looking for more runtime information about connected USB units is to run the command "dmesg" after plugging in the device. You can also look for and/or install custom kernel extensions supporting specific types of USB devices.

One common cause of problems with USB devices on iOS devices is that the USB port only delivers a very small amount of power. Many USB devices require more power than this port can provide. You'll then need to plug the USB device into a powered USB hub, and then connect the hub with the camera adapter to the iOS device.