There are "sheep dip" kiosks that are designed to inspect and even sanitise USB and other storage devices. So, before you plug the storage device into the computer, you plug it into the kiosk first, which tests it, sanitises it, and clears it for use.
I know of several high-security environments that use something like this. I'm sure there are other vendors, but I've seen OPSWAT most often.
This is on top of the basic controls on the computer, like disabling auto-run, having an agent on the computer that only allows file transfer from the device and blocks all direct access to files or executables, etc.