@JeremyCherfas That's mighty odd. Part of my backup routine on the Men's Shed iMac is to perform CCC & Time Machine backups to partitions on an external HD & another CCC backup to an external USB 3 SSD. When booted from the latter none of the apps try to work from the internal HD.
As for erasing the internal, can't you just select it from Disk Utility and erase it from there?