Troubleshooting & messages · Moving, offloading and restoring apps
Why can't I move Storage Studio itself to the external drive?
Short answer: Storage Studio must stay on your Mac to manage the drive, even when the drive is unplugged, so it can't move itself. To remove it, use More → Uninstall Storage Studio….
Storage Studio has to be on your Mac to manage your drive — including the moments the drive isn't connected and when it needs to put things back. Moving it to the drive it manages would break that, so it's never offered.
If you want to remove Storage Studio, use More → Uninstall Storage Studio…, which tidies up properly.